# Nowhere dense subset

From Topospaces

*This article defines a property over pairs of a topological space and a subspace, or equivalently, properties over subspace embeddings (viz, subsets) in topological spaces*

## Definition

### Symbol-free definition

A subset of a topological space is said to be **nowhere dense** if the interior of its closure is empty.

A nowhere dense closed subset is the same as the complement of a dense open subset. In general, the complement of a nowhere dense subset is dense, but the complement of a dense subset need not be nowhere dense.