Loading...
Thumbnail Image
Item

Topologies induced by metrics with disconnected range

Abstract
In a metric space (X, d) a ball B(x, ε) is separated if d(B(x, ε), X\B(x, ε)] > 0. If the separated balls form a sub-base for the d-topology then Ind X = 0. The metric is gap-like at x if dx(X) is not dense in any neighbourhood of 0 in [0, ∞). The usual metric on the irrational numbers, P, is the uniform limit of compatible metrics (dn), each dn being gap-like on P. In a completely metrizable space X if each dense Gδ is an Fσ then Ind X = 0. © 1982, Australian Mathematical Society. All rights reserved.
Type
Journal Article
Type of thesis
Series
Citation
Broughan, K. A. (1982). Topologies induced by metrics with disconnected range. Bulletin of the Australian Mathematical Society, 25(1), 133–142. http://doi.org/10.1017/S0004972700005116
Date
1982
Publisher
Degree
Supervisors
Rights
This article is published in the Bulletin of the Australian Mathematical Society. Used with permission.