Embedding of partially ordered topological spaces in Fell topological hyperspaces

TL;DR

This paper investigates how certain partially ordered topological spaces can be embedded into Fell topological hyperspaces, highlighting conditions for continuity and providing counterexamples for other topologies.

Contribution

It establishes a theorem on embedding partially ordered topological spaces into Fell hyperspaces and explores the continuity issues with Vietoris and Hausdorff topologies.

Findings

Embedding theorem for partially ordered topological spaces in Fell hyperspaces

Counterexamples showing non-continuity in Vietoris and Hausdorff topologies

Insights into topological properties of hyperspaces and embeddings

Abstract

In this paper, we prove a theorem about embedding of some partially ordered topological spaces in topological hyperspaces equipped with Fell topology. Then we give some examples to show that the map defining the embedding may not be continuous with respect to Vietoris topology or Hausdorff topology equipped on the hyperspaces.