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Encyclopedia
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Separated Sets: Encyclopedia - Separated Sets
In topology and related branches of mathematics, separated sets are pairs of subsets of a given topological space that are related to eac...
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Encyclopedia
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Separated Sets: Encyclopedia Ii - Separated Sets - Definitions
There are various versions of the concept. The terms are defined below, where X is a topological space.
First, two subsets A and B of X a...
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Encyclopedia
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List Of General Topology Topics: Encyclopedia Ii - List Of General Topology Topics - Topological Properties
List of general topology topics - Compactness and countability.
Compact space
Relatively compact subspace
Heine-Borel theorem
Tychono...
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Encyclopedia
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Separation Axiom: Encyclopedia Ii - Separation Axiom - Definitions Of The Axioms
Many of these names have alternative meanings in some of mathematical literature, as explained on History of the separation axioms; for e...
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Encyclopedia
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Separation Axiom: Encyclopedia Ii - Separation Axiom - Other Separation Axioms
There are some other conditions on topological spaces that are sometimes classified with the separation axioms, but these don't fit in wi...
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Encyclopedia
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Separation Axiom: Encyclopedia Ii - Separation Axiom - Relationships Between The Axioms
The T0 axiom is special in that it cannot only be added to a property (so that regular plus T0 is T3) but also subtracted from a property...
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Encyclopedia
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Separation Axiom: Encyclopedia Ii - Separation Axiom - Separated Sets And Topologically Distinguishable Points
The separation axioms are about the use of topological means to distinguish disjoint sets and distinct points. It's not enough for elemen...
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Encyclopedia
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Separated Sets: Encyclopedia Ii - Separated Sets - Relation To Connected Spaces
Given a topological space X, it is sometimes useful to consider whether it is possible for a subset A to be separated from its complement...
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Encyclopedia
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Separated Sets: Encyclopedia Ii - Separated Sets - Relation To Separation Axioms And Separated Spaces
The separation axioms are various conditions that are sometimes imposed upon topological spaces which can be described in terms of the va...
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