On a modification of finite-dimensional Niemytzki spaces

TL;DR

This paper extends the Niemytzki plane construction to higher dimensions and investigates related topologies on the Euclidean half-space, analyzing their properties and relationships.

Contribution

It introduces a higher-dimensional generalization of the Niemytzki space and studies a poset of related topologies, expanding understanding of their structure.

Findings

Extended Niemytzki space to dimensions n ≥ 3

Analyzed properties of topologies in the poset

Established relationships between these topologies

Abstract

In this paper we extend the construction of the Niemytzki plane to dimension $n \geq 3$. Further, we consider a poset of topologies on the closed $n$-dimensional Euclidean half-space similar to one from \cite{AAK} which is related to the Niemytzki plane topology. Then we explore properties of topologies from the poset.