Separable extensions of first countable spaces
Certain equivalences of Mrowka's separating condition enable us to characterize when parametric maps are open, closed or quotient.
Arhangel’skii [Sci. Math. Jpn. 55 (2002), 153–201] defined notions of relative paracompactness in terms of locally finite open partial refinement and asked if one can generalize the notions above to the well known Michael’s criteria of paracompactness in [17] and [18]. In this paper, we consider some versions of relative paracompactness defined by locally finite (not necessarily open) partial refinement or locally finite closed partial refinement, and also consider closure-preserving cases, such...
We characterize spaces with --linked bases as specially embedded subspaces of separable spaces, and derive some corollaries, such as the -productivity of the property of having a -linked base.