S-paracompact

Definition

Let S be a class of spaces closed under taking homeomorphic images. A space X is said to be S-paracompact iff XxY is normal for every Y in S.

Definition2

A topological space is called S-paracompact if every open cover of X has a locally finite semiopen refinement.

Reference

Definition 1

Scott, Brian M., More about orthocompactness., Topology, Proc. Conf., Vol. 5, Birmingham/Ala. 1980, 155-184 (1981).

Definition 2

Khalid Y. Al-Zoubi, S-paracompact spaces, Acta Math. Hungar. Vol. 110, No. 1-2, pp.165-174.