In [2] (page 27) Engelking states that:

The Niemytzki plane was defined (and attributed to Niemytzki), by Alexandroff and Hopf in [1]

which is accurate since in [1], where the plane is defined there is a footnote attributing that example to Niemytzki.

Does anyone know whether there is an article or book by Niemyzki where he defines the plane?


[1] Alexandroff, P., Hopf, H., Topologie I, Berlin 1935.

[2] R. Engelking, General Topology, Heldermann Verlag, Berlin, Sigma Series in Pure Mathematics 6, 1989.


V. Niemytzki, Über die Axiome des metrischen Raumes (1931) [see page 670]

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  • $\begingroup$ Thanks a lot. This is very helpful. I wonder if in this article it was the first time he defined it. $\endgroup$ – Sergio Garcia Oct 5 '17 at 0:40
  • $\begingroup$ there is an earlier paper: V. Niemytzki, On the third axiom of metric spaces (1927). $\endgroup$ – Carlo Beenakker Oct 5 '17 at 6:20
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    $\begingroup$ I checked this one before but it seems the plane is not defined there. BUT, I think the first reference you sent me (1931), is kind of the second part of the other (1927). It's likely that the (1931) is the first time he defined on a paper. Thanks for your help. $\endgroup$ – Sergio Garcia Oct 7 '17 at 14:32

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