Category:Definitions/Homeomorphisms (Metric Spaces)
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This category contains definitions related to homeomorphisms in the context of metric spaces.
Related results can be found in Category:Homeomorphisms (Metric Spaces).
Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ 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 "Definitions/Homeomorphisms (Metric Spaces)"
The following 9 pages are in this category, out of 9 total.
H
- Definition:Homeomorphic Metric Spaces
- Definition:Homeomorphism (Metric Spaces)/Also known as
- Definition:Homeomorphism/Metric Spaces
- Definition:Homeomorphism/Metric Spaces/Definition 1
- Definition:Homeomorphism/Metric Spaces/Definition 2
- Definition:Homeomorphism/Metric Spaces/Definition 3
- Definition:Homeomorphism/Metric Spaces/Definition 4