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Topic: Completely regular space

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	Kids.Net.Au - Encyclopedia > Completely regular
		In topology and related brances of mathematics, Tychonoff spaces and completely regular spaces are particularly nice kinds of topological spaces.
		Completely regular spaces and Tychonoff spaces are related through the notion of Kolmogorov equivalence.
		Complete regularity and Tychonoff-ness are preserved by taking initial topologies[?].
	www.kids.net.au /encyclopedia-wiki/co/Completely_regular (426 words)

	Regular space
		(Hausdorffness); all are equivalent in the context of regular spaces.
		Most topological spaces studied in mathematical analysis are regular; in fact, they are usually completely regular, which is a stronger condition.
		space that is not Hausdorff (and hence not preregular) cannot be regular.
	www.ebroadcast.com.au /lookup/encyclopedia/t3/T3_space.html (917 words)

	NationMaster - Encyclopedia: Tychonoff space
		In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are particularly nice kinds of topological spaces.
		X is a completely regular space iff, given any closed set F and any point x that does not belong to F, there is a continuous function f from X to the real line R such that f(x) is 0 and f(y) is 1 for every y in F.
		In mathematics, a manifold M is a type of space, characterized in one of two equivalent ways: near every point of the space, we have a coordinate system; or near every point, the environment is like that in Euclidean space of a given dimension.
	www.nationmaster.com /encyclopedia/Tychonoff-space (1987 words)

	PlanetMath: Tychonoff space
		It can be proved that a topological space is Tychonoff if and only if it has a Hausdorff compactification.
		Tikhonov space, Tychonoff topological space, Tikhonov topological space, Tychonov space, Tychonov topological space
		This is version 7 of Tychonoff space, born on 2002-01-22, modified 2006-10-13.
	www.planetmath.org /encyclopedia/TikhonovTopologicalSpace.html (206 words)

	Tychonoff space
		In topology and related brances of mathematics, Tychonoff spaces and completely regular spaces are particularly nice kinds of topological spaces.
		Completely regular spaces and Tychonoff spaces are related through the notion of Kolmogorov equivalence.
		Almost every topological space studied in mathematical analysis is Tychonoff, or at least completely regular.
	www.ebroadcast.com.au /lookup/encyclopedia/ty/Tychonoff_space.html (401 words)

	[No title]
		X is a subspace of a normal space d.
		If X is regular then for any non-convergent sequence in X there are disjoint closed sets A and B in X each of which contains some subsequence.
		Since X is regular, X-A contains a closed nbhd B of X. Since x is a limit point, B contains a subsequence.
	www.lehigh.edu /~dmd1/yr1013.txt (1401 words)

	PlanetMath: separation axioms (Site not responding. Last check: 2007-11-03)
		The separation axioms are additional conditions which may be required to a topological space in order to ensure that some particular types of sets can be separated by open sets, thus avoiding certain pathological cases.
		spaces in the way we defined normal spaces (and vice-versa); there is no consensus on this issue.
		See Also: normal, Hausdorff space not completely Hausdorff, Sierpinski space, metric spaces are Hausdorff, zero dimensional, Hausdorff space, regular space,
	planetmath.org /encyclopedia/Regular.html (509 words)

	PlanetMath: Tychonoff space (Site not responding. Last check: 2007-11-03)
		It can be proved that a topological space is Tychonoff if and only if it has a Hausdorff compactification.
		Tikhonov space, Tychonoff topological space, Tikhonov topological space, Tychonov space, Tychonov topological space
		This is version 7 of Tychonoff space, born on 2002-01-22, modified 2006-10-13.
	planetmath.org /encyclopedia/CompletelyRegular.html (206 words)

	[No title]
		Before humans went into space, animals were sent up in rockets as surrogates to help us understand if a living being could withstand and survive a journey beyond the Earth's protective environment.
		While these animals were in space, instruments monitored various physiological responses as the animals experienced the stresses of launch, reentry, and the weightless environment.
		As the first spacecraft that could be used again and again, the space shuttle has provided space life scientists with a more regular opportunity to conduct experiments aimed at a deeper understanding of the human body.
	www.nsbri.org /HumanPhysSpace/focus1/legacy.html (1478 words)

	Springer Online Reference Works
		An extension of a topological space which is a compact space.
		The importance of the theory of compactifications is explained by the fundamental role of compact spaces in topology and functional analysis.
		As regards imbedding in compactifications, it is finally-compact spaces which are dual with spaces of countable type.
	eom.springer.de /c/c023550.htm (1691 words)

	Tychonoff space - Wikipedia, the free encyclopedia
		In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are particularly nice kinds of topological spaces.
		X is a completely regular space if and only if, given any closed set F and any point x that does not belong to F, there is a continuous function f from X to the real line R such that f(x) is 0 and f(y) is 1 for every y in F.
		It is characterised by the universal property that, given a continuous map f from X to any other compact Hausdorff space Y, there is a unique continuous map g from βX to Y that extends f in the sense that f is the composition of g and j.
	en.wikipedia.org /wiki/Tychonoff_space (639 words)

	Springer Online Reference Works
		In the class of completely-regular spaces, the perfect mappings are characterized by the fact that their Stone–Čech extension maps remainders to remainders (cf.
		Weight of a topological space) of the image is always equal to that of the pre-image, and the Suslin number of the image is equal to that of the pre-image.
		If a topological space can be mapped perfectly onto one metric space and compressed onto another metric space (which need not be the same), then it is itself metrizable.
	eom.springer.de /p/p072060.htm (388 words)

	Newsvine - space
		Space shuttle Discovery and its seven astronauts safely returned to Earth on Friday after some last-minute suspense over which landing site to use, closing out a year in which NASA finally got construction of the international space station back on track.
		Thrill-seekers looking to blast into space would need to be informed in writing of serious risks — including death — and promise not to sue the government under the first-ever rules for commercial space travel.
		Space weather forecasters revised their predictions for storminess Wednesday after a major flare erupted on the Sun overnight, threatening damage to communication systems and power grids while offering up the wonder of the Northern Lights.
	www.newsvine.com /space (1945 words)

	Tenntop Abstracts
		Distance spaces are a generalization of metric spaces, obtained by replacing the nonnegative integers as distances by elements of a partially ordered, commutative monoid.
		A continuity space is a set X with a (not necessarily symmetric) distance function valued in an ordered abelian semigroup (\cal V,+,\leq) with least element and identity 0, greatest absorbing element \infty, and satisfying d(x,x)=0, d(x,z)\leq d(x,y)+d(y,z).
		Thus the non-commutativity of A and the asymmetry of topologies on the ideal spaces of A are intimately intertwined.
	math.tntech.edu /tenntop/abstracts.html (4721 words)

	Space Traffic Control (Site not responding. Last check: 2007-11-03)
		This connection between space object control and space operations is key to understanding the vision outlined in the pages that follow.
		Space object identification will be conducted through one or more of the following methods: spectral signature analysis using low to medium (spatial, but high multi/hyper/ultra/omni-spectral) resolution sensors, deployment of higher spatial resolution sensors, or use of medium resolution sensors to produce interferometric images.
		This paper recommends the military services turn the attention of their space doctrinal development organizations to assessing the impact of emerging technologies as described herein, with the goal of building a joint doctrine driving coordinated space system development instead of merely adapting to the limits of current systems.
	www.au.af.mil /Spacecast/app-d/app-d.html (8594 words)

	Space and Time
		Yet the fl hole that forms is completely independent of the type of matter and rapidly loses all the multipole moments except the first two: the monopole moment, which is the mass,and the dipole moment, which is the angular momentum.
		However, in my picture, this loss of phase- space volume is balanced by a process of "spontaneous" quantum measurement in which information is gained and phase-space volumes increase.
		PHASE SPACE A phase-space diagram is a mathematical volume of many dimensions formed when coordinate axes are assigned to each of the distance and momentum values of each particle.
	members.fortunecity.com /templarser/space.html (4186 words)

	FAH Excerpt: Separation (Site not responding. Last check: 2007-11-03)
		The two entries in each row of the chart are closely related: a space satisfies the condition in the left column if and only if the space is Kolmogorov and satisfies the condition in the right column in the same row.
		spaces, but the abstract theory can be developed more clearly if we classify properties according to the various axioms in the chart.
		space'', and ``completely regular Hausdorff space'' are used interchangeably in the literature; they all describe the same thing.
	www.math.vanderbilt.edu /~schectex/ccc/excerpts/separat.html (481 words)

	[No title]
		These missions have sought to determine, in detail, how space flight influences living things, so that the health and productivity of space travelers can be maintained and so that lessons in medicine and physiology learned in space can be transferred back to Earth to enrich all our lives.
		This Focus examines an actual space flight investigation which flew in both the SLS-1 mission and the SLS-2 mission and was designed to examine how the operation of the cardiovascular system is changed in space when astronauts are at rest and when they are exercising.
		And finally, it illustrates an important space study that was carried out to see how and why the muscles of astronauts can change their very character as they adapt to the new environment of space where the natural gravitational pull is absent.
	www.nsbri.org /HumanPhysSpace/contents/overview.html (774 words)

	NASA - Space Rocks
		The three main types of space rocks are comets, asteroids and meteoroids.
		A meteor, or shooting star, is a streak of light that is caused by the friction when a meteoroid from space enters the Earth's atmosphere.
		And, meteorites are space rocks that survive the friction of the atmosphere and land on Earth.
	www.nasa.gov /audience/forstudents/5-8/features/F_Space_Rocks.html (869 words)

	Yorkshire CND - Space Debris Mitigation: The Case For A Code Of Conduct - 15/4/05
		Launch vehicle lower stages generally fall back into the atmosphere and completely burn up, providing a tidy, if fiery, solution but the typical fate of rocket upper stages, which are usually cast off after launch, is to blow up.
		Over time, and in the harsh environment of space, the mechanical integrity of the booster's internal components breaks down; lines leak, corrosive fuel seeps into nooks and crevices, micro and not-so-micro meteoroids strike and penetrate.
		Space debris is a regular agenda item at meetings of UNCOPUOS (UN Committee on the Peaceful Uses of Outer Space) and the IAA (International Academy of Astronautics) and ESA's own quadrennial space debris conference has become the world's largest forum dedicated solely to debris.
	www.cndyorks.gn.apc.org /yspace/articles/debris_code_needed.htm (1580 words)

	Selections and suborderability by G. Artico, U. Marconi, J.Pelant, L. Rotter, and M. Tkachenko (Site not responding. Last check: 2007-11-03)
		A selection on an Hausdorff space X is a Vietoris continuous selection on all non-empty closed subsets of X. A weak selection is a continuous selection on all subsets consisting of one or two points.
		Furthermore, a sequentially compact suborderable space is not necessarily orderable.
		There exists a locally compact locally countable space with a zero-selection and Cantor-Bendixson height equal to 2 which is not normal.
	at.yorku.ca /i/a/a/i/09.htm (509 words)

	SPACE.com -- Hubble Space Telescope Helps Pin Down Beginning of Time
		A group of researchers using the Hubble Space Telescope today claimed a more accurate measurement of the beginning of time, an extremely important but highly debated cosmic birth date.
		Because galaxies are all moving away from each other, a discovery made by Edwin Hubble in the late 1920s, leading theorists have long figured things all originated in one point in space, billions of years ago, in a Big Bang.
		But age estimates based on this expanding universe typically range from 12 billion to 15 billion years, with each new study working from a slightly different set of numbers as more data is gathered on the rate of expansion.
	www.space.com /scienceastronomy/astronomy/age_universe_020424.html (981 words)

	The Guardians.com - Peace in Space
		You are doing your daily exercise in the recreation module, but you will have go to the bio-med lab for a physical check-up at regular intervals during your three- or six-month stay.
		Experiments are carried out to discover what happens to living things in space, to find ways of preventing serious irreversible effects on future space travellers.
		Astronauts can actually grow a little in space, and this can happen to you after a night's sleep, because you are lying down.
	www.theguardians.com /space/orbitalmech/gm_ssbml.htm (751 words)

	Kennedy Space Center Ticket Store- Admission, Launch Viewing & Astronaut Training Experience (ATX)
		SM Due to Tropical Storm Ernesto, Kennedy Space Center Visitor Complex and U.S. Astronaut Hall of Fame will be closed on Tuesday, August 29, and Wednesday, August 30th, 2006.
		On launch day, currently scheduled for July 4, 2006, Kennedy Space Center Visitor Complex will be open and accessable only to guests who purchased or received launch viewing tickets and a parking placard.
		Saturday, May 5- Space history will be made as Hall of Fame Astronauts including John Glenn, Jim Lovell and John Young will gather to induct three of America’s finest Space Shuttle commanders into the U.S. Astronaut Hall of Fame.
	www.ksctickets.com (788 words)

	[No title]
		] A concept in decision theory which states that for a class of decision functions to be complete it must include a uniformly better decision function, which is a decision function that is sometimes better but never worse (according to some criterion) than each decision function not in the class.
		] A space which is represented as a union of simplices which intersect only on their faces.
		] Analysis of the climate of a single space, or comparison of the climates of two or more places, by the relative frequencies of various weather types or groups of such types; a type is defined by the simultaneous occurrence within specified narrow limits of each of several weather elements.
	www.accessscience.com /Dictionary/C/C40/DictC40.html (1483 words)

	Space Clearing online store (Site not responding. Last check: 2007-11-03)
		Space Clearing is a specialized branch of Feng Shui that works at even deeper levels to clear and consecrate the energies of buildings.
		Many people now choose to do this ceremony as part of their regular building maintenance programme so that the space is energetically as well as physically clean and clear.
		She uses them in her own professional consultation work and can confidently say that they are all of the finest quality she has found anywhere in the world for this purpose.
	www.spaceclearing.com /ecom/products.asp?store=us (2515 words)

	Web hosting: Hagen Hosting for your web hosting needs
		Hagen Hosting is professionally managed by adults, unlike many of the so-called "kiddie host" web hosting "companies" that are completely unregistered and run by kids living in their parents' basement using cheap rented desktop computers as their "servers".
		We also include anti-virus filtering to prevent nasty viruses and worms from infecting your computer, as well as continuously updated anti-phishing technologies to prevent fraudsters from draining your bank account, stealing your identity, or otherwise defrauding you.
		The dirty little secret of the web hosting industry is that very few actually do, because it requires expensive infrastructure investments and requires highly skilled and highly paid technical professionals to implement and maintain them.
	www.hagenhosting.com (931 words)

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