| Title |
Constructing a metric according to urysohn's metrization theorem |
| Translation of Title |
Metrikos konstrukcija pagal Urisono metrizacijos teoremą. |
| Authors |
Labinas, Markas |
| Full Text |
|
| Pages |
22 |
| Keywords [eng] |
topology, separable metrizable space, totally bounded metric space, Urysohn’s metrization theorem, metric construction |
| Abstract [eng] |
For separable metrizable spaces we define metrics, called Urysohn constructs, resulting from spe cific naturally ordered collections of continuous functions and sequences of positive reals converging to 0. The definition is motivated by the proof of Urysohn’s metrization theorem. We first prove that for any separable metric space there exists an Urysohn construct bounding the initial metric from below. Next, we show that for any totally bounded metric space there exists an Urysohn construct that uniformly approximates the initial metric from below with arbitrary accuracy. |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Master thesis |
| Language |
English |
| Publication date |
2026 |
