Connected-weakly open subset

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.

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.

Relation with other properties

Stronger properties

• Open subset

Weaker properties

• Path-connected-weakly open subset