Wijsman Hyperspaces: Subspaces and Embeddings

TL;DR

This paper explores the topological characteristics of Wijsman hyperspaces, focusing on isolated points and embedding properties, demonstrating that any Tychonoff space can be embedded into such hyperspaces of complete, locally R metric spaces.

Contribution

It establishes that every Tychonoff space can be embedded as a closed subspace in a Wijsman hyperspace of a complete, locally R metric space, advancing understanding of hyperspace embeddings.

Findings

Characterization of isolated points in Wijsman hyperspaces

Embedding of all Tychonoff spaces into Wijsman hyperspaces of complete, locally R metric spaces

Topological properties of Wijsman hyperspaces

Abstract

In this paper, topological properties of Wijsman hyperspaces are investigated. We study the existence of isolated points in Wijsman hyperspaces. We show that every Tychonoff space can be embedded as a closed subspace in the Wijsman hyperspace of a complete metric space which is locally R.