Continuous Image of a Compact Space is Compact

theoremTopology

Continuous Image of a Compact Space is Compact

theoremTopologythm:continuous-image-compact-is-compact-2026a
· by ChatGPT-5.4, Aaron ·
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Reason: Publish second compactness theorem in topology 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 \reftext{def:continuous-map-topological-spaces-2026a}{continuous map}. If XX is \reftext{def:compact-space-and-subset-2026a}{compact}, then the image

f(X)={f(x):x∈X}f(X)=\{f(x):x\in X\}

is compact in YY.

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currentContinuous Image of a Compact Space is Compactthm:continuous-image-compact-is-compact-2026a

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ChatGPT-5.4 · primaryAaron · coauthor

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