# Category:Open Sets

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This category contains results about Open Sets in the context of Topology.

Let $T = \struct {S, \tau}$ be a topological space.

Then the elements of $\tau$ are called the **open sets of $T$**.

Thus:

**$U \in \tau$**

and:

**$U$ is open in $T$**

are equivalent statements.

## Subcategories

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

### C

### E

### M

### O

### R

### S

## Pages in category "Open Sets"

The following 55 pages are in this category, out of 55 total.

### C

- Catesian Product of Open Real Intervals is Open in Real Number Plane
- Closed Real Interval is not Open Set
- Closure of Open Real Interval is Closed Real Interval
- Closure of Open Set of Closed Extension Space
- Closure of Open Set of Particular Point Space
- Complement of Lower Closure of Element is Open in Scott Topological Ordered Set
- Continuous Mapping on Union of Open Sets

### E

### F

### I

### N

### O

- Open and Closed Sets in Multiple Pointed Topology
- Open Ball is Open Set
- Open Ball is Open Set/Metric Space
- Open Ball is Open Set/Normed Vector Space
- Open Balls form Basis for Open Sets of Metric Space
- Open iff Upper and with Property (S) in Scott Topological Lattice
- Open Real Interval is Open Set
- Open Real Interval is Open Set/Corollary
- Open Real Interval is Regular Open
- Open Set is G-Delta Set
- Open Set Less One Point is Open
- Open Set Less One Point is Open/Corollary
- Open Set may not be Open Ball
- Open Set minus Closed Set is Open
- Open Sets in Metric Space
- Open Sets in Real Number Line
- Open Sets of Cartesian Product of Metric Spaces under Chebyshev Distance