Timeline for The functor of continuous functions from compact CW-spaces to the reals
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 30, 2018 at 16:33 | comment | added | Robert Furber | @roger123 Every paracompact Hausdorff space admits a complete uniformity (see Kelley's General Topology Chapter 6, exercise L (d)), so a paracompact Hausdorff space is realcompact iff it has no discrete subset of (2-valued) measurable cardinality by Shirota's theorem. (See, for instance Gillman and Jerison's Rings of Continuous Functions Theorem 15.20). Therefore it is consistent that every paracompact Hausdorff space is realcompact. | |
| Oct 30, 2018 at 15:18 | history | edited | Todd Trimble | CC BY-SA 4.0 |
Link (to a website that pirates copyrighted works according to a prominent MO user) removed
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| Nov 1, 2010 at 12:48 | comment | added | roger123 | Thank you. Paracompactness does not suffice here, right? | |
| Oct 29, 2010 at 8:43 | vote | accept | roger123 | ||
| Oct 28, 2010 at 20:13 | comment | added | David Roberts♦ | For reference: en.wikipedia.org/wiki/Realcompact_space | |
| Oct 28, 2010 at 15:53 | history | answered | Dmitri Pavlov | CC BY-SA 2.5 |