On pairwise paracompactness

Journal of the Australian Mathematical Society

M. Ganster¹ 

[1] I. L. Reilly

关键词: 54 D 18;    54 E 55;   

DOI  :  10.1017/S1446788700035850

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

This paper answers a recent question concerning the relationship between two notions of paracompactness for bitopological spaces. Romaguera and Marin defined pairwise paracompactness in terms of pair open covers, motivated by a characterization of paracompactness due to Junnila. On the other hand, Raghavan and Reilly defined a bitopological space (X, τ, σ) to be δ-pairwise paracompact if and only if every τ open (σ open) cover of X admits a τ V σ open refinement which is τ V σ locally finite. It is shown that pairwise paracompactness implies δ-pairwise paracompactness, and that the converse is false.

【 授权许可】

Unknown