# Category:Homeomorphisms

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This category contains results about Homeomorphisms.

Definitions specific to this category can be found in Definitions/Homeomorphisms.

$f$ is a **homeomorphism** if and only if both $f$ and $f^{-1}$ are continuous.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### H

### S

### T

## Pages in category "Homeomorphisms"

The following 29 pages are in this category, out of 29 total.

### C

- Completely Hausdorff Space is Preserved under Homeomorphism
- Completely Normal Space is Preserved under Homeomorphism
- Composite of Homeomorphisms is Homeomorphism
- Continuous Bijection from Compact to Hausdorff is Homeomorphism
- Continuous Bijection from Compact to Hausdorff is Homeomorphism/Corollary
- Continuous Involution is Homeomorphism

### H

### I

### R

### S

### T

- T0 Space is Preserved under Homeomorphism
- T1 Space is Preserved under Homeomorphism
- T2 Space is Preserved under Homeomorphism
- T3 1/2 Space is Preserved under Homeomorphism
- T3 Space is Preserved under Homeomorphism
- T4 Space is Preserved under Homeomorphism
- T5 Space is Preserved under Homeomorphism
- Topologies induced by Usual Metric and Scaled Euclidean Metric on Positive Integers are Homeomorphic
- Tychonoff Space is Preserved under Homeomorphism