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    $\begingroup$ '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'. $\endgroup$ Commented Mar 17, 2023 at 19:05
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    $\begingroup$ 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. $\endgroup$ Commented Mar 17, 2023 at 19:56
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    $\begingroup$ 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. $\endgroup$ Commented May 9, 2024 at 0:16
  • $\begingroup$ This is the first example that came to my mind. $\endgroup$ Commented May 9, 2024 at 0:36