
	Where results make sense

Topic: Hausdorff maximality theorem

Related Topics

Total order

Dense

Hausdorff

Topology glossary

Hausdorff space

Tychonoff space

Dual space

Felix Hausdorff

In the News (Tue 8 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Felix Hausdorff - Wikipedia, the free encyclopedia
		Felix Hausdorff (November 8, 1868 – January 26, 1942) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory and functional analysis.
		Hausdorff studied in Leipzig and taught mathematics there until 1910, when he became professor of mathematics in Bonn.
		When the Nazis came to power, Hausdorff, who was Jewish, felt that as a respected university professor he would be spared from persecution.
	en.wikipedia.org /wiki/Felix_Hausdorff (181 words)

	halting problem - Article and Reference from OnPedia.com
		Yet another, quite amazing, consequence of the undecidability of the halting problem is Rice's theorem which states that the truth of any non-trivial statement about the function that is defined by an algorithm is undecidable.
		The concepts raised by Gdel's incompleteness theorems are very similar to those raised by the halting problem, and the proofs are quite similar.
		This weaker form differs from the standard statement of the incompleteness theorem by asserting that a complete, consistent and sound axiomatization of all statements about natural numbers is unachievable.
	www.onpedia.com /encyclopedia/halting-problem (2611 words)

	HAUSDORFF (Site not responding. Last check: 2007-11-06)
		The Hausdorff dimension agrees with the ordinary (topological) dimension on "well-behaved sets", but it is applicable to many more sets and is not always a natural number.
		In fact, Hausdorff's original definition of topological space required all topological spaces to be Hausdorff (a requirement that is not made today).
		Pseudometric spaces typically are not Hausdorff, but they are preregular, and their use in analysis is usually only in the construction of Hausdorff gauge spaces.
	www.websters-online-dictionary.org /definition/HAUSDORFF (1317 words)

	Hausdorff Article, Hausdorff Information (Site not responding. Last check: 2007-11-06)
		Felix Hausdorff (November 8, 1868 - January 26, 1942) was aGerman mathematician who is considered to be one of the founders ofmodern topology and who contributed significantly to set theory and functional analysis.
		Whenthe Nazis came to power, Hausdorff, who was Jewish, felt that as a respected universityprofessor he would be spared from persecution.
		When in 1942 he could nolonger avoid being sent to a concentration camp, Hausdorff committed suicide togetherwith his wife and sister-in-law.
	www.anoca.org /he/mathematics/hausdorff.html (222 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		It uses both Zorn's lemma and Hausdorff's Maximality Theorem (which are both equivalent to the Axiom of Choice).
		Another classical use of Tychonoff'Theorem in functional analysis is Banach-Alaoglu's Theorem: In the dual space of a Banach space, the unit ball is compact for its weak topology.
		For the more common application involving Hausdorff spaces, the theorem is equivalent to "the Prime Ideal Theorem", which says, in one form, that every non-trivial filter in a Boolean algebra can be extended to an ultrafilter.
	www.math.niu.edu /~rusin/known-math/95/tychonoff (488 words)

	Felix Hausdorff - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		Felix Hausdorff (November 8 1868 - January 26 1942) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory and functional analysis.
		When in 1942 he could no longer avoid being sent to a concentration camp, Hausdorff committed suicide together with his wife and sister-in-law.
		This page was last modified 01:58, 16 Jun 2005.
	northmiami.us /project/wikipedia/index.php/Felix_Hausdorff (207 words)

	C-algebras and E-theory (Site not responding. Last check: 2007-11-06)*
		Up to Theorem 1.31, we have only used 'an appropriate version of Urysohn's lemma' in Example 1.19; such a version is Proposition 15 on p.
		To understand the statement of Theorem 1.31 in the notes, you need to know what the weak*-topology of the dual space is. The relevant material can be found on pp.
		While Alaglu's theorem is not needed to understand the statement, it is certainly necessary in order to understand the proof.
	home.imf.au.dk /matkt/E-th2-history.html (1112 words)

	[No title]
		If {X} is a compact Hausdorff space and F is an equicontinuous, pointwise bounded subset of the space C(X) of continuous functions on X, then F is totally bounded in the uniform metric and the closure of F in C(X) is compact.
		It is equivalent to: 1) Zorn's Lemma; 2) the Hausdorff Maximality Theorem; 3) the well-ordering
		This theorem establishes both that there are different sizes of infinity, and that there is no greatest such “size.” Cantor's proof was the first use of a diagonalization argument to derive a contradiction.
	www.mathacademy.com /platonic_realms/encyclop/main.txt (8404 words)

	Applied Functional Analysis and Partial Differential Equations by Milan Miklavcic
		The Cauchy Theorem is also used in a couple of places, with the most difficult version used in (4.44).
		With regard to the writing style, all formal statements, like Theorems, contain all assumptions except for those declared at the beginning of the section in which the statement appears.
		The Hille-Yosida Theorem for strongly continuous semigroups and Hille's construction of analytic semigroups are presented.
	www.mth.msu.edu /~milan/bk1.html (931 words)

	Glossary — PAIAS
		an axiom is a postulate (proposition or theorem) assumed to be
		A formal theory has (formally described) axioms and rules of inference from which are derived the (other) theorems of the theory.
		Their theorem used to prove this result used the Axiom of Choice.
	paias.org /glossary.htm (2789 words)

	List of mathematical theorems article - List of mathematical theorems mathematical theorems list theorems Abelian ... (Site not responding. Last check: 2007-11-06)
		List of mathematical theorems article - List of mathematical theorems mathematical theorems list theorems Abelian tauberian theorems - What-Means.com
		See defect (geometry) for another theorem of Descartes.
		List of mathematical theorems article - List of mathematical theorems definition - what means List of mathematical theorems
	www.what-means.com /encyclopedia/List_of_mathematical_theorems (67 words)

	Math 7200
		Note that Zorn's lemma and the Hausdorff Maximality Principle are simply two versions of the same result.
		This consists of the basic definition of a group, examples (some of which will be presented in class) of groups, subgroups, order of groups and elements, the fundamental theorem on cyclic groups, cosets and Lagrange's theorem.
		This week we will be continuing the study of rings, including the fundamental theorem of arithmetic (unique factorization into primes) for PID's, examples of Euclidean rings and the Euclidean algorithm in such rings, and Gauss's lemma on irreducible polynomials in Z[X].
	www.math.lsu.edu /~adkins/m7200.html (932 words)

	malawi.ca - Hausdorff distance (Site not responding. Last check: 2007-11-06)
		We explain what is Hausdorff distance, an give an algorithm for computing it in linear time for convex polygons.
		Given two sets of points and, the Hausdorff distance is defined as.
		h(A,B) is called the directed Hausdorff `distance' from A to B (this func...
	www.malawi.ca /Hausdorff-distance/all/search (88 words)

	Business Software Review : Article 'Infinite descending chain' (Site not responding. Last check: 2007-11-06)
		Duality In the previous definitions, we often noted that a concept can be defined by just inverting the ordering in a former definition.
		This is the case for "least" and "greatest", for "minimal" and "maximal", for "upper bound" and "lower bound", and so on.
		This is a general situation in order theory: A given order can be inverted by just exchanging its direction, pictorially flipping the Hasse diagram top-down.
	www.business-software-review.org /DisplayArticle42500.html (858 words)

	<Data Minds> - tribe.net (Site not responding. Last check: 2007-11-06)
		A self-evident or universally recognized truth; a maxim: “It is an economic axiom as old as the hills that goods and services can be paid for only with goods and services” (Albert Jay Nock).
		A self-evident principle or one that is accepted as true without proof as the basis for argument; a postulate.
		The Löwenheim-Skolem theorems tell us that if we restrict ourselves to first-order logic, any axiom system for the reals admits other models, including both models that are smaller than the reals and models that are larger.
	lovechao.tribe.net /thread/b117884e-cfcf-414c-a8ff-fd5be7fb0705 (2315 words)

	List of axioms -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		Equivalents of AC (Click link for more info and facts about Hausdorff maximality theorem) Hausdorff maximality theorem
		(Click link for more info and facts about Boolean prime ideal theorem) Boolean prime ideal theorem
		Alternates incompatible with AC (Click link for more info and facts about Axiom of real determinacy) Axiom of real determinacy
	www.absoluteastronomy.com /encyclopedia/L/Li/List_of_axioms.htm (956 words)

Try your search on: Qwika (all wikis)