| dc.contributor.author | Broughan, Kevin A. | en_NZ |
| dc.date.accessioned | 2016-07-01T04:45:55Z | |
| dc.date.available | 1982 | en_NZ |
| dc.date.available | 2016-07-01T04:45:55Z | |
| dc.date.issued | 1982 | en_NZ |
| dc.identifier.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 | en |
| dc.identifier.issn | 0004-9727 | en_NZ |
| dc.identifier.uri | https://hdl.handle.net/10289/10500 | |
| dc.description.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. | en_NZ |
| dc.format.mimetype | application/pdf | |
| dc.language.iso | en | |
| dc.rights | This article is published in the Bulletin of the Australian Mathematical Society. Used with permission. | |
| dc.title | Topologies induced by metrics with disconnected range | en_NZ |
| dc.type | Journal Article | |
| dc.identifier.doi | 10.1017/S0004972700005116 | en_NZ |
| dc.relation.isPartOf | Bulletin of the Australian Mathematical Society | en_NZ |
| pubs.begin-page | 133 | |
| pubs.elements-id | 139400 | |
| pubs.end-page | 142 | |
| pubs.issue | 1 | en_NZ |
| pubs.volume | 25 | en_NZ |
| dc.identifier.eissn | 1755-1633 | en_NZ |
