Timeline for Relation between two different definitions for relative sequential compactness
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| Aug 7 at 14:18 | vote | accept | yada | ||
| Nov 16, 2023 at 22:31 | answer | added | Pietro Majer | timeline score: 2 | |
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Aug 12, 2016 at 19:40 | comment | added | Taras Banakh | In Functional Analysis there is a widely used notion of an angelic space, introduced by Fremlin: this is a space in which a relatively countably compact space is relatively compact and compact subsets are Frechet-Urysohn. In such spaces both notions of sequential compactness seem to coincide. More information on angelic spaces can be found in the book [J.Kąkol, W.Kubiś, M.López-Pellicer, Descriptive topology in selected topics of functional analysis. Developments in Mathematics, 24. Springer, New York, 2011]. | |
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| Jan 8, 2016 at 16:32 | comment | added | PassingThru | The standard sources that I have seen all use definition 2. As pointed out in the linked math.so item, with definition 1 you could have a sequentially compact set that is not relatively so. And in applying the Eberlein-Smulian theorem, there may be situations where you want to assume only the property in definition 2. | |
| Jan 8, 2016 at 14:20 | history | edited | yada | CC BY-SA 3.0 |
added a reference for a second counterexample
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| Jan 8, 2016 at 8:06 | answer | added | Dominic van der Zypen | timeline score: 1 | |
| Jan 8, 2016 at 7:30 | history | asked | yada | CC BY-SA 3.0 |