On $n$-dimensional Niemytzki spaces

Vitalij Chatyrko

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.

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