# A Niemytzky-Tychonoff theorem for all topological spaces

Research output: Contribution to journal › Article › peer-review

### Standard

**A Niemytzky-Tychonoff theorem for all topological spaces.** / Weiss, Ittay.

Research output: Contribution to journal › Article › peer-review

### Harvard

*Topology Proceedings*, vol. 51, pp. 55-60. <http://topology.auburn.edu/tp/reprints/v51/tp51004p1.pdf>

### APA

*Topology Proceedings*,

*51*, 55-60. http://topology.auburn.edu/tp/reprints/v51/tp51004p1.pdf

### Vancouver

### Author

### Bibtex

}

### RIS

TY - JOUR

T1 - A Niemytzky-Tychonoff theorem for all topological spaces

AU - Weiss, Ittay

PY - 2018/4

Y1 - 2018/4

N2 - The classical Niemytzky-Tychonoff theorem characterises compactness of a metrisable topological space by means of the completeness of all of the metrics inducing the topology. Motivated by results of Kopperman and Flagg to the effect that every topological space is metrisable, as long as metrisability is suitably modified to allow the metric to take values more general than real numbers, we show that the Niemytzky-Tychonoff theorem remains true under this broader notion of metrisability, thus obtaining a metric characterisation of compactness valid for all topological spaces.

AB - The classical Niemytzky-Tychonoff theorem characterises compactness of a metrisable topological space by means of the completeness of all of the metrics inducing the topology. Motivated by results of Kopperman and Flagg to the effect that every topological space is metrisable, as long as metrisability is suitably modified to allow the metric to take values more general than real numbers, we show that the Niemytzky-Tychonoff theorem remains true under this broader notion of metrisability, thus obtaining a metric characterisation of compactness valid for all topological spaces.

KW - pub_permission_granted

UR - http://topology.auburn.edu/tp/

M3 - Article

VL - 51

SP - 55

EP - 60

JO - Topology Proceedings

JF - Topology Proceedings

SN - 0146-4124

ER -

ID: 7770429