Heine-Cantor theorem

By the Heine-Cantor theorem it is uniformly continuous in that set.

This is a generalization of the Heine-Cantor theorem mentioned above, since .

The fact that a continuous function on a compact interval 'I' is necessarily uniformly continuous (the Heine-Cantor theorem) admits a succinct non-standard proof.

In mathematics, the Heine-Cantor theorem, named after Eduard Heine and Georg Cantor, its statement is as follows:

A consequence is a generalisation of the Heine-Cantor theorem: each continuous function from a compact Hausdorff space to a uniform space is uniformly continuous.