Timeline for An example of a regular but not linear-based topological space
Current License: CC BY-SA 3.0
12 events
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| Apr 26, 2018 at 14:11 | comment | added | Rafał Gruszczyński | @EvgenyKuznetsov This freely available paper by Dimiter Vakarelov may be a good starting point: link.springer.com/chapter/10.1007%2F978-0-387-69245-6_6 | |
| Apr 26, 2018 at 11:14 | comment | added | Evgeny Kuznetsov | @Mad Hatter Thanks for feedback to, very interesting comment of you, that forced me to look for a reference of such methods for BCA-s, can you provide me with that? | |
| Apr 26, 2018 at 10:44 | comment | added | Rafał Gruszczyński | In my case the interest in such spaces stems from point-free topology, especially the part of it dealing with the so-called Boolean Contact Algebras. Point-free counterparts of linear bases (i.e. certain chains in BCAs) are good approximations of points and linear-based spaces are used for representation theorems for BCAs (at least in my studies of BCAs, there are different approaches too). As far as I know there is no book nor paper devoted to class of linear-based spaces. But check the so-called well-based spaces and radial spaces which are related to linear-based. | |
| Apr 26, 2018 at 10:27 | comment | added | HenrikRüping | I am not aware of it. | |
| Apr 26, 2018 at 10:25 | comment | added | Evgeny Kuznetsov | @HenrikRüping thanks for feedback. Is the notion of linaerly based spaces as a subclass of spaces such usable to be considered somewhere in literature on general topology? If so what is possible reference? | |
| Apr 26, 2018 at 10:10 | comment | added | HenrikRüping | Clearly all metric spaces are linear based. Thus not being linear based is an obstruction to metrizability. The example I gave is an example that the second countability assumption in Urysohns metrization theorem is essential. | |
| Apr 26, 2018 at 9:06 | comment | added | Evgeny Kuznetsov | Please provide the information about where in mathematics do arrive mentioned above by you linear-based topological spaces, why are them interesting? | |
| Apr 26, 2018 at 7:56 | history | edited | Rafał Gruszczyński | CC BY-SA 3.0 |
added 4 characters in body; edited title
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| Aug 31, 2016 at 12:08 | vote | accept | Rafał Gruszczyński | ||
| Jun 3, 2016 at 11:03 | answer | added | HenrikRüping | timeline score: 6 | |
| Jun 3, 2016 at 10:43 | history | edited | Rafał Gruszczyński | CC BY-SA 3.0 |
edited title
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| Jun 3, 2016 at 10:36 | history | asked | Rafał Gruszczyński | CC BY-SA 3.0 |