On $n$-dimensional Niemytzki spaces

Abstract

In this paper we extend the construction of the Niemytzki plane to dimension $n \geq 3$ andexplore some properties of the new spaces. Furthermore, we consider a poset of topologies on the closed $n$-dimensional Euclidean half-spacesimilar to one from \cite{AAK} which is related to the Niemytzki plane topology.