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Nowadays the unique 2 point, nondiscrete, nontrivial topological space goes by the name of the Sierpinski space.

How did that space come to be named after Sierpinski?

The comments to this MathOverflow post contain some speculations on this question, but I've not been able to find anything else.

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  • $\begingroup$ The Wikipedia entry you linked has Counterexamples in Topology in its references. Did you look in there? $\endgroup$
    – Michał Miśkiewicz
    Commented Feb 15 at 16:59
  • $\begingroup$ Interesting, thanks. I can't get a hold of copy yet, but I could get an on-line copy of the table of contents which lists "Sierpinski Space". That, at least, proves that the terminology predates the web, counter to the speculations in that MathOverflow post. $\endgroup$
    – Lee Mosher
    Commented Feb 15 at 17:44
  • $\begingroup$ The earliest instance I could find with Google is: Transactions of the American Mathematical Society, 1969, p. 384: "Sierpiński space , that is , the space with two points and three open sets". Unfortunately Google does not display the actual text of the document. It does find two other publications from 1969 and 1970 that supposedly use the term, but the snippet views offered do not capture it (a frequent issue with Google snippets). But as a working hypothesis, looking for the precise origin in the 1969-1970 time frame seems the way to go. $\endgroup$
    – njuffa
    Commented Feb 15 at 23:58
  • $\begingroup$ I just looked in my copy of "Counterexamples"; the index only lists one mention of "Sierpinski Space" (topology 11, on p.44), and that page offers no historical background to it. $\endgroup$
    – Alexis
    Commented Feb 15 at 23:58
  • $\begingroup$ The term "Sierpinski space" in the 1940s was used for something else. Such spaces obey a system of axioms similar to "topology" but more general. (The intersection of two open sets need not be open.) $\endgroup$
    – Gerald Edgar
    Commented Feb 16 at 3:30

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