# Category:Definitions/Neighborhoods

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This category contains definitions related to Neighborhoods.

Related results can be found in Category:Neighborhoods.

Let $A \subseteq S$ be a subset of $S$.

A **neighborhood** of $A$, which can be denoted $N_A$, is any subset of $S$ containing an open set of $T$ which itself contains $A$.

That is:

- $\exists U \in \tau: A \subseteq U \subseteq N_A \subseteq S$

## Pages in category "Definitions/Neighborhoods"

The following 40 pages are in this category, out of 40 total.

### N

- Definition:Neighborhood (Analysis)/Metric Space
- Definition:Neighborhood (Metric Space)
- Definition:Neighborhood (Neighborhood Space)
- Definition:Neighborhood (Real Analysis)/Epsilon
- Definition:Neighborhood (Topology)
- Definition:Neighborhood (Topology)/Neighborhood defined as Open
- Definition:Neighborhood (Topology)/Point
- Definition:Neighborhood (Topology)/Set
- Definition:Neighborhood Basis
- Definition:Neighborhood Filter
- Definition:Neighborhood Filter of Set
- Definition:Neighborhood Filter/Point
- Definition:Neighborhood Filter/Set
- Definition:Neighborhood of Infinity
- Definition:Neighborhood of Infinity (Complex Analysis)
- Definition:Neighborhood of Infinity (Real Analysis)
- Definition:Neighborhood of Infinity (Real Analysis)/Negative Infinity
- Definition:Neighborhood of Infinity (Real Analysis)/Positive Infinity
- Definition:Neighborhood of Infinity (Topology)
- Definition:Neighborhood of Negative Infinity
- Definition:Neighborhood of Point
- Definition:Neighborhood of Positive Infinity
- Definition:Neighborhood of Set
- Definition:Neighborhood Space
- Definition:Neighborhood Space Induced by Topological Space
- Definition:Neighborhood Sub-Basis

### O

- Definition:Open Neighborhood
- Definition:Open Neighborhood in Real Euclidean Space
- Definition:Open Neighborhood of Point in Topological Space
- Definition:Open Neighborhood/Real Analysis
- Definition:Open Neighborhood/Real Analysis/Real Euclidean Space
- Definition:Open Neighborhood/Real Analysis/Real Numbers
- Definition:Open Neighborhood/Topology
- Definition:Open Set (Neighborhood Space)