Characterizations of Quasi-Metrizable Bitopological Spaces

Journal of the Australian Mathematical Society

T. G. Raghavan¹ 

[1]I. L. Reilly

关键词: 54 E 55;   

DOI  :  10.1017/S1446788700029864

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

In this paper we prove that a pairwise Hausdorff bitopological spaceis quasi-metrizable if and only if for each point x ∈ X and for i, j = 1,2, i ≠ j, one can assignnbd bases { S(n, i; x) | n = 1, 2,… } such that (i) y ∉ S (n − 1, i; x) imples S(n, i; x) ∩ S (n, j; y) = φ, (ii) y ∈ S (n, i; x) implies S (n, i; y) ⊂ S(n − 1, i; x). We derive two further results from this.

【 授权许可】

Unknown