# Category:T1 Spaces

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This category contains results about $T_1$ (Fréchet) spaces in the context of Topology.

$\left({S, \tau}\right)$ is a **Fréchet space** or **$T_1$ space** if and only if:

- $\forall x, y \in S$ such that $x \ne y$, both:
- $\exists U \in \tau: x \in U, y \notin U$

- and:
- $\exists V \in \tau: y \in V, x \notin V$

## Subcategories

This category has the following 4 subcategories, out of 4 total.

### C

### F

### N

## Pages in category "T1 Spaces"

The following 43 pages are in this category, out of 43 total.

### C

### D

### E

### F

### N

### T

- T1 Property is Hereditary
- T1 Space is Preserved under Closed Bijection
- T1 Space is Preserved under Homeomorphism
- T1 Space is T0 Space
- T1 Space is T1/2 Space
- T1 Space is Weakly Countably Compact iff Countably Compact
- T2 Space is T1 Space
- Topological Group is T1 iff T2
- Totally Disconnected Space is T1
- Tychonoff Space is Regular, T2 and T1