Interior-preserving collection

Definition
A collection of subsets of a topological space is termed an interior-preserving collection or a Q-collection if for any point in the topological space, the intersection of all the member subsets containing it, is open.

Stronger properties
If the collection comprises open sets, the following properties are stronger:


 * Finite collection
 * Locally finite collection
 * Point-finite collection

Related compactness property
The compactness properties related to interior-preserving open covers are:


 * Orthocompact space
 * Countably orthocompact space