Definition 5.25.1 (Compactification).label Let $X$ be a topological space, then a compactification of $X$ is a pair $(Y, f)$ where
- (1)
$Y$ is a compact Hausdorff space.
- (2)
$f \in C(X; Y)$ is an embedding.
- (3)
$f(X)$ is dense in $Y$.
Definition 5.25.1 (Compactification).label Let $X$ be a topological space, then a compactification of $X$ is a pair $(Y, f)$ where
$Y$ is a compact Hausdorff space.
$f \in C(X; Y)$ is an embedding.
$f(X)$ is dense in $Y$.
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