Path-connected-weakly open subset

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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 path-connected-weakly open if it satisfies the following equivalent conditions:

Significance

We can replace open subsets with path-connected-weakly open subsets, for homology computation tools like Mayer-Vietoris homology sequence and excision.

Relation with other properties

Stronger properties