# Category:Homeomorphic Metric Spaces

This category contains results about Homeomorphic Metric Spaces.

Let $M_1 = \left({A_1, d_1}\right)$ and $M_2 = \left({A_2, d_2}\right)$ be metric spaces.

Let $f: A_1 \to A_2$ be a bijection such that:

$f$ is continuous from $M_1$ to $M_2$
$f^{-1}$ is continuous from $M_2$ to $M_1$.

Then:

$f$ is a homeomorphism
$M_1$ and $M_2$ are homeomorphic.

## Pages in category "Homeomorphic Metric Spaces"

The following 15 pages are in this category, out of 15 total.