TOP (category)
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Definition
\mathrm{TOP} is the category of all topological spaces, the objects are tuples of a set X and a topology \mathcal{J}_X on X and the arrows, or morphisms of the category are continuous functions[1]. More explicitly.
- The objects of \mathrm{TOP} are all topological spaces, (X,\mathcal{J}_X)
- The arrows/morphisms of \mathrm{TOP} are the continuous functions between spaces.
Discussion
TODO: Discuss as a subcategory of \mathrm{SET} , remember it must first go under the forgetful functor to discard the topological structure and distill it to just sets and mappings
References
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