[Home]T0-spaces

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Abbreviation: Top0

Definition

A T0-space is a topological space X = (X,Ω(X)) such that
for every pair of distinct points in the space, there is an open set containing one but not the other:   x,y ∈ X  ⇒  ∃U ∈ Ω(X)[(x ∈ U and y ∉ U) or (y ∈ U and x ∉ U)].

Morphisms

Let X and Y be T0-spaces. A morphism from X to Y is a function f : XY that is continuous: V ∈ Ω(Y)  ⇒  f−1[V] ∈ Ω(X).

Some results

Examples

Properties

Classtypesecond-order
Amalgamation propertyyes
Strong amalgamation propertyno
Epimorphisms are surjectiveno

Remark: The properties given above use an (E,M) factorization system with E =  surjective morphisms and M =  embeddings.

Subclasses

T1-spaces

Superclasses

Topological spaces

References

http://www.wikipedia.org/wiki/Topology_glossary


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Last edited August 22, 2003 10:17 pm (diff)
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