Topological structures of hyperspaces of finite sets in non-separable metrizable spaces

Katsuhisa Koshino

Topological structures of hyperspaces of finite sets in non-separable metrizable spaces

General Topology 2015-12-08 v3

Authors: Katsuhisa Koshino

Abstract

Let ${\rm Fin}(X)$ be the hyperspace consisting of non-empty finite subsets of a space $X$ endowed with the Vietoris topology. In this paper, we characterize a metrizable space $X$ whose hyperspace ${\rm Fin}(X)$ is homeomorphic to the linear subspace spanned by the canonical orthonormal basis of a non-separable Hilbert space.

Keywords

hyperspace of finite sets Vietoris topology non-separable metrizable space Hilbert space homeomorphism topological structure

Cite

@article{arxiv.1508.07788,
  title  = {Topological structures of hyperspaces of finite sets in non-separable metrizable spaces},
  author = {Katsuhisa Koshino},
  journal= {arXiv preprint arXiv:1508.07788},
  year   = {2015}
}

Comments

Lemma 4.1 and Proposition 4.2 has been revised because there is a gap in the proof. arXiv admin note: substantial text overlap with arXiv:1503.08575

Topological structures of hyperspaces of finite sets in non-separable metrizable spaces

Abstract

Keywords

Cite

Comments

Related papers