I have been looking for a digital version of the following article: "S. Mrowka, On universal spaces, Bull Acad. Polon. Sci., cl. III, 4 (1956) 479-481". There is a MathSciNet review made by J. Isbell here: On universal spaces, but that's pretty much all I could find online. If any of you know where to get this paper, I'd really appreciate it if you could point me in the right direction.
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1$\begingroup$ the journal has not been digitized, but many libraries have it: worldcat.org/title/… $\endgroup$– Carlo BeenakkerFeb 28, 2022 at 17:59
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1$\begingroup$ Or see Problems 2.7.7.and 2.7.8 in Engelking's General Topology $\endgroup$– KP HartFeb 28, 2022 at 18:17
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$\begingroup$ Thank you both for your comments. In Isbell's review it says: "It is shown that for every cardinal $m$ there is a $T_1$-space which admits no non-constant continuous mapping into a $T_1$-space of power less than $m$". I was hoping to read exactly what Mrówka had done, but from Carlo's comment I guess that's going to be very difficult. $\endgroup$– PelusoFeb 28, 2022 at 18:42
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2$\begingroup$ that journal is notoriously difficult to obtain papers from. you will likely have to submit a request through your university library. $\endgroup$– D.S. LiphamMar 1, 2022 at 21:16
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1$\begingroup$ My guess: take a set $X$ of cardinality larger than $m$ with the co-finite topology. Then if $Y$ is $T_1$ of cardinality less than $m$ and $f:X\to Y$ is continuous then there is a $y$ such that $f^{-1}(y)$ is infinite; as it is also closed it must be all of $X$. $\endgroup$– KP HartMar 1, 2022 at 21:26
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