Timeline for Which closed subsets $Y$ of a compact space $X$ admit a linear extensor $C(Y)\to C(X)$?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 3 at 7:06 | comment | added | Tyrone | Thanks for the correction, @KPHart. | |
| Mar 3 at 7:05 | history | edited | Tyrone | CC BY-SA 4.0 |
added 67 characters in body
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| Mar 1 at 9:00 | comment | added | KP Hart | The cellularity of $\beta\mathbb{N}\setminus\mathbb{N}$ is equal to $2^{\aleph_0}$ rather than $\aleph_1$. | |
| Feb 22 at 8:23 | comment | added | Pietro Majer | In fact what I’m mostly interested is when X is a compact Hausdorff space with no other assumptions: what can be said on the family of its closed subsets A for which there exists a linear bounded extender? (e.g. question 2, and question 3 , added now). On the Corollary: so it gives another proof of $c_0$ not being complemented in $\ell_\infty$, ritgth? | |
| Feb 22 at 8:06 | comment | added | Pietro Majer | Thank you for the detailed answer! The existence of a continuous extender is in fact a consequence of Tietze (the restriction operator $C(X)\to C(Y)$ being surjective), because every surjective bounded linear operator between Banach space, admits a continuous right inverse (in general nonlinear, nor differentiable) . | |
| Feb 22 at 7:57 | history | answered | Tyrone | CC BY-SA 4.0 |