The Niemytzki plane is kappa-metrizable

TL;DR

This paper explores the relationship between stratifiable and κ-metrizable spaces, providing a characterization of the latter and constructing a κ-metric for the Niemytzki plane based on Euclidean properties.

Contribution

It offers a new characterization of κ-metrizable spaces and introduces a κ-metric for the Niemytzki plane, expanding understanding of these topological concepts.

Findings

Characterization of κ-metrizable spaces modeled on Chigogidze's work

Construction of a κ-metric for the Niemytzki plane

Clarification of differences between stratifiable and κ-metrizable spaces

Abstract

We try to explain the differences between the concepts of stratifiable space and $\varkappa$-metrizable space. In particular, we give a characterization of $\varkappa$-metrizable spaces which is modelled on Chigogidze's characterization. Moreover, we present a $\varkappa$-metric for the Niemytzki plane, using the properties of the Euclidean metric.