Connected-weakly open subset

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.

Stronger properties

 * Open subset

Weaker properties

 * Path-connected-weakly open subset