Compactness is a Topological Invariant
# Statement
Suppose $X, Y$ are Topological Spaces and $X \cong Y$. Then $X$ is compact If and Only If $Y$ is.
# Proof
Continuous Functions Preserve Compactness $\blacksquare$
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Suppose $X, Y$ are Topological Spaces and $X \cong Y$. Then $X$ is compact If and Only If $Y$ is.
Continuous Functions Preserve Compactness $\blacksquare$