Countably orthocompact space

Symbol-free definition
A topological space is said to be countably orthocompact if every countable open cover of it has an interior-preserving open refinement.

Formalisms
A refinement formal expression for countable orthocompactness is:

Countable open $$\to$$ Interior-preserving open

Stronger properties

 * Countably compact space
 * Orthocompact space
 * P-space