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Good old Steen and Seebach discuss the Smirnov deleted sequence topology in their Counterexamples in Topology (2nd ed. 1978).

This is also reported as the $K$-topology, in e.g. Wikipedia etc.

However, none of the sources that I've found tell us which particular Smirnov is behind it.

I am guessing it's Yurii Mikhailovich Smirnov as of all the Smirnovs I know of in mathematics, he is the one who has greatest involvement in topology.

(For example: Vladimir Ivanovich is known for a 5-volume textbook, and Nikolai Vasilyevich made a name for himself in statistics.)

Yurii Mikhailovich is of course the mathematician whose name is associated with the Nagata-Smirnov metrization theorem, so it's more than plausible it's the same one.

Can anyone point me towards a source that can confirm this?

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  • $\begingroup$ It's probably not Yakov Smirnov but I suppose you can't be too sure $\endgroup$
    – Ben Grossmann
    Commented Jun 1, 2020 at 15:50
  • $\begingroup$ Considering the provenance of Tom Lehrer, I can't fault your logic. :-) $\endgroup$
    – Prime Mover
    Commented Jun 1, 2020 at 15:54
  • $\begingroup$ He must have been active around 1929, as he's credited with the example in a paper from around that time. The metrisation theorem is from the fifties. $\endgroup$
    – Henno Brandsma
    Commented Jun 1, 2020 at 16:47
  • $\begingroup$ @Henno Brandsma: Any source for that? The metrization paper includes this example of a topology, sure, but the 1951 paper does not actually make any reference to any 1929 paper. My Russian's a but rusty so it will take effort to make sense of the 1951 paper. $\endgroup$
    – Prime Mover
    Commented Jun 1, 2020 at 19:41
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    $\begingroup$ It’s in Mémoire sur des espaces topologiques compacts. By Alexandroff & Urysohn and they credit it to Smirnov IiRC that’s a French paper do a lot easier. $\endgroup$
    – Henno Brandsma
    Commented Jun 1, 2020 at 19:45

1 Answer 1

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It is Yurii Mikhailovich Smirnov: the space is Example $1$ in his paper О МЕТРИЗАЦИИ ТОПОЛОГИЧЕСКИХ ПРОСТРАНСТВ (On metrization of topological spaces), Uspekhi Matem. Nauk, 1951, 6, 100-111. It’s on p. 107 at the end of Section 2.

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  • $\begingroup$ In light of this and Henno's research, I'll go with this reference. Until I manage to get hold of a copy of the 1929 document and confirm this topology is or is not in there, I'll assume that the 1951 ref is the first time it's detailed. Thx. $\endgroup$
    – Prime Mover
    Commented Jun 1, 2020 at 21:11
  • $\begingroup$ @PrimeMover: My pleasure. $\endgroup$
    – Brian M. Scott
    Commented Jun 1, 2020 at 21:14
  • $\begingroup$ @PrimeMover It's translated in Smirnov Yu. M. On metrization of topological spaces Amer. Math. Soc. Transl. 8 (Ser. 1) 63–77 (thx to Engelking). Engelking (General Topology 2nd ed.) treats the example in 1.5.6 but gives no reference in the historical notes, which is atypical. $\endgroup$
    – Henno Brandsma
    Commented Jun 1, 2020 at 21:39
  • $\begingroup$ Yes, that's the 1951 reference, I've got that, that's not a problem, it's the 1929 dissertation I haven't been able to lay my hands on. Besides, all I really need is just confirmation of which Smirnov this topology was named after, and I think it's fair to go with Yu.M. $\endgroup$
    – Prime Mover
    Commented Jun 1, 2020 at 21:45

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