Timeline for Is there a Tychonoff space $X$ of cardinality not of the form $2^\alpha$ such that $|C(X)| = |X|$
Current License: CC BY-SA 3.0
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| Sep 14, 2013 at 17:55 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Sep 14, 2013 at 14:06 | comment | added | Joel David Hamkins | @Silvi, the same argument works even if you don't have the final point, since every continuous function $\kappa\to\mathbb{R}$ is eventually constant, because $\kappa$ has uncountable cofinality. So we would also have $|C(Y)|=\kappa$. But in this case, $Y$ would not be compact, although still Tychonoff. | |
| Sep 14, 2013 at 13:52 | comment | added | user37834 | +1 Nice. If $Y = \kappa$ ($\kappa$ as above) then what is the cardinality of $C(Y)$? Is it $\kappa$ !? | |
| Sep 14, 2013 at 12:41 | vote | accept | CommunityBot | ||
| Sep 14, 2013 at 12:12 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |