Other Properties
- The monomorphisms in Top are the injective continuous maps, the epimorphisms are the surjective continuous maps, and the isomorphisms are the homeomorphisms.
- The extremal monomorphisms are (up to isomorphism) the subspace embeddings. Every extremal monomorphism is regular.
- The extremal epimorphisms are (essentially) the quotient maps. Every extremal epimorphism is regular.
- There are no zero morphisms in Top, and in particular the category is not preadditive.
- Top is not cartesian closed (and therefore also not a topos) since it does not have exponential objects for all spaces.
Read more about this topic: Category Of Topological Spaces
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