# Category:Set Interiors

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This category contains results about Set Interiors in the context of Topology.

Definitions specific to this category can be found in Definitions/Set Interiors.

The **interior** of $H$ is the union of all subsets of $H$ which are open in $T$.

That is, the **interior** of $H$ is defined as:

- $\displaystyle H^\circ := \bigcup_{K \mathop \in \mathbb K} K$

where $\mathbb K = \set {K \in \tau: K \subseteq H}$.

## Subcategories

This category has only the following subcategory.

### I

## Pages in category "Set Interiors"

The following 31 pages are in this category, out of 31 total.

### C

### E

### I

- Interior equals Complement of Closure of Complement
- Interior is Subset of Exterior of Exterior
- Interior is Subset of Interior of Closure
- Interior may not equal Exterior of Exterior
- Interior of Closed Real Interval is Open Real Interval
- Interior of Closed Set of Particular Point Space
- Interior of Closure of Interior of Union of Adjacent Open Intervals
- Interior of Finite Intersection equals Intersection of Interiors
- Interior of Intersection may not equal Intersection of Interiors
- Interior of Open Set
- Interior of Singleton in Real Number Line is Empty
- Interior of Subset
- Interior of Subset of Double Pointed Topological Space
- Interior of Subset of Indiscrete Space
- Interior of Union is not necessarily Union of Interiors
- Interior of Union of Adjacent Open Intervals
- Intersection of Interiors contains Interior of Intersection

### K

- Kuratowski's Closure-Complement Problem/Closure of Interior
- Kuratowski's Closure-Complement Problem/Closure of Interior of Closure
- Kuratowski's Closure-Complement Problem/Closure of Interior of Complement
- Kuratowski's Closure-Complement Problem/Interior
- Kuratowski's Closure-Complement Problem/Interior of Closure
- Kuratowski's Closure-Complement Problem/Interior of Closure of Interior
- Kuratowski's Closure-Complement Problem/Interior of Complement of Interior