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Separability axioms and metric-like functions
| Content Provider | Scilit |
|---|---|
| Author | Anton, Howard |
| Copyright Year | 1976 |
| Description | We call a topological space completely regular if points and closed sets can be separated by continuous real-valued functions, and we call a topological space Tychonoff or $T_{3α}$ if it is $T^{1}$ and completely regular. It is well known that the Tychonoff spaces are precisely the gauge spaces, that is the topological spaces whose topologies are induced by separating families of pseudometrics. V.G. Boltjanskiĭ has given analogous characterizations for $T_{0}$, $T_{1}$, $T_{2}$, regular, and $regular-T_{1}$ spaces in terms of families of “metric-like” functions. The purpose of this note is to fill in a case missing in Boltjanskiĭ's paper, the completely regular spaces, and to relate Boltjanskiĭ's work to results on quasi-uniformization by William J. Pervin and results about semi-gauge spaces by J.V. Michalowicz. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FA938C408B0B7359A7759AB8656FEDC4/S0004972700022620a.pdf/div-class-title-separability-axioms-and-metric-like-functions-div.pdf |
| Ending Page | 271 |
| Page Count | 7 |
| Starting Page | 265 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700022620 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 2 |
| Volume Number | 15 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1976-10-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Applied Mathematics Metric Like Topological Space Space Tychonoff Gauge Spaces Completely Regular Spaces |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
