When is a P-space weakly discretely generated

作者：Alas Ofelia T; Junqueira Lucia R; Wilson Richard G^*

来源：Topology and Its Applications, 2014, 163: 2-10.

DOI：10.1016/j.topol.2013.10.001

• Discretely generated space
• Weakly discretely generated space
• P-space
• Lindelof space
• Countable extent
• Frechet net character

A space X is discretely generated at a point x is an element of X if for any A subset of X with x is an element of cl(A), there exists a discrete set D subset of A such that x is an element of cl(D). The space X is discretely generated if it is discretely generated at every point x is an element of X. We say that X is weakly discretely generated if for any non-closed set A subset of X, there exists a discrete set D subset of A such that cl(D)\A not equal empty set. We obtain new results concerning these properties in the class of P-spaces.

• 出版日期2014-2-15