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Separated sets - Relation to separation axioms and separated spaces | | Separated sets - Relation to separation axioms and separated spaces: 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 various types of separated sets. As an example, we will define the T2 axiom, which is the condition imposed on separated spaces. Specifically, a topological space is separated if, given any two distinct points x and y, the singleton sets {x} and {y} are separated by neighbourhoods.
Separated spaces are also called Hausdorff spaces or T ...
See also:Separated sets, Separated sets - Definitions, Separated sets - Relation to separation axioms and separated spaces, Separated sets - Relation to connected spaces, Separated sets - Relation to topologically distinguishable points | | | Separated sets, Separated sets - Definitions, Separated sets - Relation to connected spaces, Separated sets - Relation to separation axioms and separated spaces, Separated sets - Relation to topologically distinguishable points | | |
| | | Separated sets: Encyclopedia II - Separated sets - Relation to separation axioms and separated spaces
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 various types of separated sets. As an example, we will define the T2 axiom, which is the condition imposed on separated spaces. Specifically, a topological space is separated if, given any two distinct points x and y, the singleton sets {x} and {y} are separated by neighbourhoods.
Separated spaces are also called Hausdorff spaces or T2 spaces. Further discussion of separated spaces may be found in the article Hausdorff space. General discussion of the various separation axioms is in the article Separation axiom.
Other related archives1/2, Connected space, Disjoint sets, Hausdorff space, Separation axiom, Topological distinguishability, Topology, closed, closure, complement, connected spaces, continuous function, distinct, empty set, if, intersection, intervals, mathematics, neighbourhood, open, open set, positive real number, preimage, real line, separable spaces, separated spaces, separation axioms, set theory, singleton sets, subset, subsets, topological space, topology, unit interval
 Adapted from the Wikipedia article "Relation to separation axioms and separated spaces", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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