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Homesubspace topology

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# subspace topology

Let $X$ be a topological space, and let $Y\subset X$ be a subset. The subspace topology on $Y$ is the topology whose open sets are those subsets of $Y$ which equal $U\cap Y$ for some open set $U\subset X$.

In this context, the topological space $Y$ obtained by taking the subspace topology is called a topological subspace, or simply subspace, of $X$.

Defines:

topological subspace, subspace

Synonym:

relative topology

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

54B05*no label found*15A66

*no label found*11E88

*no label found*

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