A note on Raghavan-Reilly's pairwise paracompactness

Abstract

The bitopological unstability of RR-pairwise paracompactness in presence of pairwise Hausdorff separation axiom is caused by a bitopological property which is much weaker and more local than RR-pairwise paracompactness. We slightly generalize some Michael's constructions and characterize RR-pairwise paracompactness in terms of bitopological θ-regularity, and some other weaker modifications of pairwise paracompactness.

Keywords

• Spaces with more topologies
• θ-regularity
• pairwise paracompactness.