On some modifications of the Niemytzki plane

TL;DR

This paper investigates how certain modifications to the Niemytzki plane, specifically replacing tangent discs with triangles of bounded angles, affect its topological properties, showing such changes alter its homeomorphism class.

Contribution

It provides a criterion for comparing modifications of the Niemytzki plane and demonstrates that replacing tangent discs with bounded-angle triangles results in a non-homeomorphic space.

Findings

Replacing tangent discs with bounded-angle triangles changes the Niemytzki plane's topology.

The modified space is not homeomorphic to the original Niemytzki plane.

A criterion for comparing such modifications is established.

Abstract

We present a criterion that compares modifications of the Niemytzki plane. It follows that if usual tangent discs of the Niemytzki plane are replaced by triangles with bounded angles, then the resulting space is not homeomorphic to the former.