Timeline for answer to Are there any other examples where "weak" and "strong" are confused in mathematics? by R. van Dobben de Bruyn
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 9, 2024 at 0:36 | comment | added | ming tsai | This is the first example that came to my mind. | |
| May 9, 2024 at 0:16 | comment | added | Tom Goodwillie | I like to say that those who call a coarse topology "strong" are thinking of the topology as something that holds the points together, while those who call a fine topology "strong" are thinking of it as something that keeps the points apart. | |
| Mar 17, 2023 at 19:56 | comment | added | Pietro Majer | but I wonder how many people would really call "stronger" a coarser topology. My guess is very few. I think the situation is not symmetric. | |
| Mar 17, 2023 at 19:05 | comment | added | Zerox | 'Weak topology' occurs when the situation is at the lower edge of continuity (with the minimal number of continuous maps): For a topological space $X$, the finer the topology on $X$ is, the less possibility of continuity a map $f$ with target $X$ will have; Conversely, the coarser the topology on $X$ is, the less possibility of continuity a map $f$ with source $X$ will have. Similarly, 'strong topology' occurs when the situation is at the upper edge of continuity. In this sense, the use of 'strong' and 'weak' is subtle, but not quite 'confused'. | |
| Mar 17, 2023 at 14:25 | history | answered | R. van Dobben de Bruyn | CC BY-SA 4.0 |