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Topic: Preregular space


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  Hausdorff space - Wikipedia, the free encyclopedia
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.
In contrast, non-preregular spaces are encountered much more frequently in abstract algebra and algebraic geometry, in particular as the Zariski topology on an algebraic variety or the spectrum of a ring.
Compact preregular spaces are normal, meaning that they satisfy Urysohn's lemma and the Tietze extension theorem and have partitions of unity subordinate to locally finite open covers.
en.wikipedia.org /wiki/Hausdorff_space   (1227 words)

  
 Regular space - Wikipedia, the free encyclopedia
X is a regular space iff, given any closed set F and any point x that does not belong to F, there exists a neighbourhood U of x and a neighbourhood V of F that are disjoint.
Most topological spaces studied in mathematical analysis are regular; in fact, they are usually completely regular, which is a stronger condition.
On the other hand, spaces that are regular but not completely regular, or preregular but not regular, are usually constructed only to provide counterexamples to conjectures, showing the boundaries of possible theorems.
en.wikipedia.org /wiki/Regular_space   (942 words)

  
 t2 space   (Site not responding. Last check: )
In topology and related branches of mathematics, Hausdorff spaces and preregular spaces are particularly nice kinds of topological spaces.
space, or separated space, iff, given any distinct points x and y, there are a neighbourhood U of x and a neighbourhood V of y that are disjoint.
Similarly, a space is preregular iff all of the limits of a given net (or filter) are topologically indistinguishable.
www.yourencyclopedia.net /T2_space.html   (872 words)

  
 Reference.com/Encyclopedia/Hausdorff space
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.
In contrast, non-preregular spaces are encountered much more frequently in abstract algebra and algebraic geometry, in particular as the Zariski topology on an algebraic variety or the spectrum of a ring.
Compact preregular spaces are normal, meaning that they satisfy Urysohn's lemma and the Tietze extension theorem and have partitions of unity subordinate to locally finite open covers.
www.reference.com /browse/wiki/Hausdorff_space   (1293 words)

  
 FAH Excerpt: Separation
space, and every preregular space is also a symmetric space.
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.
www.math.vanderbilt.edu /~schectex/ccc/excerpts/separat.html   (481 words)

  
 Hausdorff space -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: )
space is a ((mathematics) any set of points that satisfy a set of postulates of some kind) topological space in which points can be separated by neighbourhoods.
X is a preregular space if any two (Click link for more info and facts about topologically distinguishable) topologically distinguishable points can be separated by neighbourhoods.
Almost all spaces encountered in (The abstract separation of a whole into its constituent parts in order to study the parts and their relations) analysis are Hausdorff; most importantly, the (Any rational or irrational number) real numbers are a Hausdorff space.
www.absoluteastronomy.com /encyclopedia/H/Ha/Hausdorff_space.htm   (1626 words)

  
 Encyclopedia: Topological space   (Site not responding. Last check: )
Every subset of a topological space can be given the subspace topology in which the open sets are the intersections of the open sets of the larger space with the subset.
In mathematics, a compact space is a space that resembles a closed and bounded subset of Euclidean space Rn in that it is small in a certain sense and contains all its limit points.
A metrizable space is a topological space that is homeomorphic to a metric space.
www.nationmaster.com /encyclopedia/Topological-space   (6141 words)

  
 [No title]   (Site not responding. Last check: )
In topology and related fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider.
In fact, in a normal space, any two disjoint sets will also be separated by a function; this is Urysohn's Lemma.
There are some other conditions on topological spaces that are sometimes classified with the separation axioms, but these don't fit in with the usual separation axioms as completely.
www.online-encyclopedia.info /encyclopedia/s/se/separation_axiom.html   (1450 words)

  
 All words on Hausdorff space
In topology and related branches of mathematics, Hausdorff spaces, also known as Urysohn spaces, and preregular spaces are kinds of topological spaces.
The points x and y, here represented by dots on opposite sides of the picture, are separated by their respective neighbourhoods U and V, here represented by disjoint open disks with the original dots at their centres.
Conversely, a topological space is preregular if and only if its Kolmogorov space is Hausdorff.
www.allwords.org /ha/hausdorff-space.html   (1079 words)

  
 Locally compact space - Wikipedia, the free encyclopedia   (Site not responding. Last check: )
Almost all locally compact spaces studied in applications are Hausdorff, and this article is thus primarily concerned with locally compact Hausdorff spaces.
Thus locally compact spaces are as useful in p-adic analysis as in classical analysis.
Quotient spaces of locally compact Hausdorff spaces are compactly generated.
www.penginus.com /index.php/Locally_compact   (1321 words)

  
 Hausdorff space   (Site not responding. Last check: )
In topology and related branches of mathematics, Hausdorff spaces and preregular spaces are kinds of topological spaces.
Limitss of sequences, netss, and filterss (when they exist) are unique in Hausdorff spaces.
Subspacess and products of Hausdorff spaces are Hausdorff, but quotient spaces of Hausdorff spaces need not be Hausdorff.
www.sciencedaily.com /encyclopedia/hausdorff_space   (891 words)

  
 HAUSDORFF   (Site not responding. Last check: )
The Hausdorff dimension is a well-defined real number for any metric space M and we always have 0 ≤ d(M) ≤ ∞.
For example, the Cantor set (a zerodimensional topological space) is a union of two copies of itself, each copy shrunk by a factor 1/3; this fact can be used to prove that its Hausdorff dimension is ln(2)/ln(3) (see natural logarithm).
The Sierpinski triangle is a union of three copies of itself, each copy shrunk by a factor of 1/2; this yields a Hausdorff dimension of ln(3)/ln(2).
www.websters-online-dictionary.org /definition/HAUSDORFF   (1317 words)

  
 Regular space   (Site not responding. Last check: )
X is a regular space iff, given any closed set F and any point x that does not belong to F, there are a neighbourhood U of x and a neighbourhood V of F that are disjoint.
Taking the interiorss of these closed neighbourhoods, we see that the regular open sets form a base for the open sets of the regular space X.
Suppose that A is a set in a topological space X and f is a continuous function from A to a regular space Y.
www.sciencedaily.com /encyclopedia/regular_space   (991 words)

  
 Locally compact space   (Site not responding. Last check: )
To be precise, a topological space X is locally compact iff every point has a local base of compact neighborhoodss.
As mentioned in Examples, any compact Hausdorff space is also locally compact, and any locally compact Hausdorff space is in fact a Tychonoff space.
More precisely, the categories of locally compact Hausdorff spaces and of commutative C* algebras are dual; this is the Gelfand-Naimark theorem.
www.theezine.net /l/locally-compact-space.html   (1271 words)

  
 Hausdorff space - Dangeruss-Industries.com
The Hausdorff condition is one in a series of separation axioms that can be imposed on a topological space, however it is the one that is most frequently used and discussed.
X is a Hausdorff space if any two distinct points of X can be separated by neighborhoods which is the reason Hausdorff spaces are also called T
Let f : X → Y be a quotient map with X a compact Hausdorff space.
www.dangeruss-industries.com /results/Hausdorff_space.html   (1248 words)

  
 Edit My Space XML 4
Space exploration is the physical exploration of outer-Earth objects and generally anything that involves the technologies, science, and politics regarding space endeavors.
A space observatory is any instrument in outer space which is used for observation of distant planets, galaxies, and other outer space objects.
X is a preregular space, or R1 space, iff, given any topologically distinguishable points x and y, x and y can be separated by neighbourhoods.
www.xml4.com /editors/Edit-My-Space.html   (3230 words)

  
 Locally compact space   (Site not responding. Last check: )
, hence Hausdorff, Topological vector space, which is infinite-dimensional, such as an infinite-dimensional Hilbert space.
The last example contrasts with the Euclidean spaces in the previous section; to be more specific, a Hausdorff topological vector space is locally compact if and only if it is finite-dimensional (in which case it is a Euclidean space).
Since every locally compact Hausdorff space X is Tychonoff, it can be embedded in a compact Hausdorff space b(X) using the Stone-Čech compactification.
en.efactory.pl /Local_compactness   (1301 words)

  
 Regular space   (Site not responding. Last check: )
X is a regular space iff, given any closed set F and any point x that doesn't belong to F, there are a neighbourhood U of x and a neighbourhood V of F that are disjoint.
Thus from a certain point of view, regularity isn't really the issue here, and we could impose a weaker condition instead to get the same result.
space that isn't Hausdorff (and hence not preregular) cannot be regular.
www.factbase.info /re/regular-space.html   (914 words)

  
 Free cum swallow Sexy Babes   (Site not responding. Last check: )
X is a Hausdorff Facial free links video Mature boob space, or T2 space, or separated space, iff, Iran sex sex Best facial product given any distinct points x and y, there are a neighbourhood U of x and a neighbourhood V of y that are disjoint.
A topological space is Hausdorff if and only if it is both preregular and T0.
Nomenclature Examples and nonexamples Almost all spaces encountered in analysis are Hausdorff; most importantly, the real numbers are a Hausdorff space.
milf.milfhunter.cn /Teen_cum/Free_cum_swallow.html   (702 words)

  
 Kolmogorov space - Unipedia   (Site not responding. Last check: )
spaces, we first define the concept of topological distinguishablity.
If X is a topological space and x and y are points in X, then x and y are topologically indistinguishable if and only if any of the following equivalent conditions hold:
Elements of The Theory of Functions and Functional Analysis Vol 1 Metric and Normed Spaces
www.unipedia.info /T0.html   (1236 words)

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