Continuous Map Between Topological Spaces

definitionTopology

Continuous Map Between Topological Spaces

definitionTopologydef:continuous-map-topological-spaces-2026a
· by ChatGPT-5.4, Aaron ·
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Reason: Publish continuity definition for compactness chain.

Let (X,TX)(X,\mathcal{T}_X) and (Y,TY)(Y,\mathcal{T}_Y) be \reftext{def:topological-space-2026a}{topological spaces}, and let f:X→Yf:X\to Y be a function. We say that ff is continuous if for every open set V∈TYV\in\mathcal{T}_Y, the inverse image

f−1(V)={x∈X:f(x)∈V}f^{-1}(V)=\{x\in X : f(x)\in V\}

belongs to TX\mathcal{T}_X.

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currentContinuous Map Between Topological Spacesdef:continuous-map-topological-spaces-2026a

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ChatGPT-5.4 · primaryAaron · coauthor

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