Topic
Completely metrizable space
About: Completely metrizable space is a research topic. Over the lifetime, 26 publications have been published within this topic receiving 261 citations.
Papers
Journal Article•
42 citations
TL;DR: The space of Radon probability measures on a metric space and its subspaces was studied in this article, and it was proved that for any completely metrizable space, the space is homeomorphic to a Hilbert space.
Abstract: We study the space of Radon probability measures on a metric space and its subspaces , and of continuous measures, discrete measures, and finitely supported measures, respectively. It is proved that for any completely metrizable space , the space is homeomorphic to a Hilbert space. A topological classification is obtained for the pairs , and , where is a metric compactum, an everywhere dense Borel subset of , an everywhere dense -set of , and an everywhere uncountable everywhere dense Borel subset of of sufficiently high Borel class. Conditions on the pair are found that are necessary and sufficient for the pair to be homeomorphic to .
40 citations
TL;DR: In this paper, it was shown that each complete metric space is the maximal point space of a continuous, bounded complete dcpo (in other common terminology, we show that such a space has a bounded complete computational model).
33 citations
1 Jan 1998
TL;DR: In this article, a short proof of the Beer-Costantini Theorem on Polishness of the Wijsman topology is given, and the space of nonempty closed subsets of X endowed with this topology was shown to be a-favorable in the strong Choquet game.
Abstract: Let X be a completely metrizable space. Then the space of nonempty closed subsets of X endowed with the Wijsman topology is a-favorable in the strong Choquet game. As a consequence, a short proof ofthe Beer-Costantini Theorem on Polishness of the Wijsman topology is given.
27 citations
1 Apr 1990
TL;DR: In this article, an n-dimensional completely metrizable AE(n)-space P(n, T) of weight T > cl was constructed with the following property: for any at most ndimensional AE space Y of weight cl are precisely the n-invertible images of the Hilbert space?2(T).
Abstract: We construct an n-dimensional completely metrizable AE(n)-space P(n, T) of weight T > cl with the following property: for any at most ndimensional completely metrizable space Y of weight cl are precisely the n-invertible images of the Hilbert space ?2(T) .
13 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 4 |
| 2020 | 1 |
| 2017 | 1 |
| 2014 | 1 |
| 2013 | 1 |
| 2009 | 2 |