# Connected-weakly open 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*

*This term is nonstandard and is being used locally within the wiki. For its use outside the wiki, please define the term when using it.*

## Contents

## Definition

A subset of a topological space is termed *connected-weakly open* if it satisfies the following equivalent conditions:

- Given any map from a connected space to the space, the inverse image of the subset is open
- The subset occurs as a union of some of the connected components of some open subset containing it.