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Niemytzki plane
Let be the Euclidean half plane , with the usual subspace topology. We enrich the topology on by throwing in open sets of the form , that is an open ball of radius around together with its point tangent to (Fig. 1).
The space endowed with the enriched topology is called the Niemytzki plane.
Some miscellaneous properties of the Niemytzki plane are
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the subspace of is discrete, hence the only convergent sequences in this subspace are constant ones;
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it is Hausdorff;
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it is completely regular;
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it is not normal.
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Mathematics Subject Classification
54-00 General reference works (handbooks, dictionaries, bibliographies, etc.)54G99 None of the above, but in MSC2010 section 54Gxx
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new image: approximation_to_sinx by jeremyboden
new question: Solving the word problem for isomorphic groups by mairiwalker
new image: LineDiagrams.jpg by m759
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May 16
new problem: Curve fitting using the Exchange Algorithm. by jeremyboden
new question: Undirected graphs and their Chromatic Number by Serchinnho


