= Compact subsets of Tychonoff spaces are C-embedded
A <continuous function> on a <compact subset> of a <Tychonoff space> extends to the whole space. Embed the space into a cube of closed unit intervals. The <Tychonoff theorem> makes the cube <compact> <Hausdorff> and thus normal. The <compact subset> is closed in that cube, so the <Tietze extension theorem> extends its bounded function to the cube. Restrict this extension to the embedded original space. Normality of the original space is unnecessary.
Back to article page
