Timeline for The usual topologies [closed]
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 5, 2016 at 21:59 | history | closed |
Michael Greinecker Steven Landsburg Michael Albanese Noah Schweber Qfwfq |
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| Sep 5, 2016 at 21:14 | review | Close votes | |||
| Sep 5, 2016 at 22:00 | |||||
| Sep 5, 2016 at 20:53 | answer | added | Gerald Edgar | timeline score: 3 | |
| Sep 5, 2016 at 20:52 | comment | added | Michael Greinecker | @LSpice The first uncountable cardinal might be smaller than the continuum. | |
| Sep 5, 2016 at 20:52 | comment | added | Neal | In short, because they're useful in other areas of mathematics (e.g. metric geometry, functional analysis, ...). The notions in topology provide a unified way of thinking about all types of convergence, wherever they arise in mathematics. So the "natural" topologies, etc., are ones that arise in other fields of mathematics, e.g. the compact-open topology arising as the topology induced by the sup norm when the spaces in question are suitably restricted. | |
| Sep 5, 2016 at 20:50 | comment | added | LSpice | This is rather like asking "why do we use the usual addition on $\mathbb R$ rather than a different one?" If we equip $\mathbb R$ with a different topology, then, as a topological space, it isn't $\mathbb R$ anymore. That is, once we call it "$\mathbb R$ with a different topology", we might as well also call it "$\mathbb C$ with a different topology", or "the first uncountable ordinal with a different topology". | |
| Sep 5, 2016 at 20:42 | history | asked | Jeyrome Sapin | CC BY-SA 3.0 |