Glossary of categories

Category of pointed topological spaces

The category of pointed topological spaces or base spaces 𝖳𝗈𝗉• ≃ ∙ ↓𝖳𝗈𝗉 consists of topological spaces with a basepoint preserving continuous maps as its morphisms. topology This is a full subcategory of the category of topological spaces with base sets 𝖳𝗈𝗉Ω consisting of topological spaces with a subset of base points as objects and base set preserving continuous maps as its morphisms, topology i.e. if 𝑓 ∈𝖳𝗈𝗉Ω(𝑋𝐴,𝑌𝐵) then 𝑓(𝐴) ⊆𝐵.

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