Definition Via Open Sets
Objects: all topological spaces, i.e., all pairs (X,T) of set X together with a collection T of subsets of X satisfying:
- The empty set and X are in T.
- The union of any collection of sets in T is also in T.
- The intersection of any pair of sets in T is also in T.
- The sets in T are the open sets.
Morphisms: all ordinary continuous functions, i.e. all functions such that the inverse image of every open set is open.
Comments: This is the ordinary category of topological spaces.
Read more about this topic: Characterizations Of The Category Of Topological Spaces
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