# Category:Separable Spaces

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This category contains results about Separable Spaces in the context of Topology.

A topological space $T = \struct {S, \tau}$ is **separable** if and only if there exists a countable subset of $S$ which is everywhere dense in $T$.

## Subcategories

This category has the following 6 subcategories, out of 6 total.

### C

### I

### R

### S

## Pages in category "Separable Spaces"

The following 47 pages are in this category, out of 47 total.

### C

- Compact Complement Topology is Separable
- Condition for Open Extension Space to be Separable
- Continuous Image of Separable Space is Separable
- Countable Complement Space is not Separable
- Countable Discrete Space is Separable
- Countable Excluded Point Space is Separable
- Countable Fort Space is Separable
- Countable Product of Separable Spaces is Separable
- Countable Space is Separable

### E

### S

- Second-Countable Space is Separable
- Separability in Uncountable Particular Point Space
- Separability is not Weakly Hereditary
- Separable Discrete Space is Countable
- Separable Metacompact Space is Lindelöf
- Separable Metric Space is Homeomorphic to Subspace of Fréchet Metric Space
- Separable Metric Space is Second-Countable
- Separable Space need not be First-Countable
- Separable Space satisfies Countable Chain Condition
- Sequentially Compact Metric Space is Separable
- Space is Separable iff Density not greater than Aleph Zero