Niemytzki plane

Let Γ be the Euclidean half plane Γ={(x,y)y0}2, with the usual subspace topology. We enrich the topologyMathworldPlanetmath on Γ by throwing in open sets of the form {(x,0)}Br(x,r), that is an open ballPlanetmathPlanetmath of radius r around (x,r) together with its point tangent to ×{0} (Fig. 1).

Figure 1: A new open set in Γ. It consists of an open disc and the point tangent to y=0.

The space Γ endowed with the enriched topology is called the Niemytzki plane.

Some miscellaneous properties of the Niemytzki plane are

Title Niemytzki plane
Canonical name NiemytzkiPlane
Date of creation 2013-03-22 13:36:53
Last modified on 2013-03-22 13:36:53
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 7
Author PrimeFan (13766)
Entry type Example
Classification msc 54-00
Classification msc 54G99
Synonym Niemytzki space