Математическое: отличие топологий от метрик - допустимая несимметричность
Авва дал ссылку на популярные посты на mathoverflow и к ним примкнувшим.
И вот там читая
https://mathoverflow.net/questions/23478/examples-of-common-false-beliefs-in-mathematics
мне понравился коммент к ветке
Any subspace of a separable topological space is separable, too." Sounds natural.
....
(and it is true of metric spaces, and natural generalizations...) -
Mariano Suárez-Álvarez
May 4, 2010 at 23:31
...
Perhaps some discontinuities between metric space theory and topology arise because when studying metric spaces, distances are mysteriously required to be symmetric, and the requirement is dropped when switching to topological spaces. So you can have a point x that has y as a limit (i.e. it is in all neighbourhoods of y) but y doesn't have x as a limit. With this idea in mind, you can make any topological space separable by adding a single point, and making it belong to all open sets. -
Marcos Cossarini
May 5, 2010 at 14:53
И вот там читая
https://mathoverflow.net/questions/23478/examples-of-common-false-beliefs-in-mathematics
мне понравился коммент к ветке
Any subspace of a separable topological space is separable, too." Sounds natural.
....
(and it is true of metric spaces, and natural generalizations...) -
Mariano Suárez-Álvarez
May 4, 2010 at 23:31
...
Perhaps some discontinuities between metric space theory and topology arise because when studying metric spaces, distances are mysteriously required to be symmetric, and the requirement is dropped when switching to topological spaces. So you can have a point x that has y as a limit (i.e. it is in all neighbourhoods of y) but y doesn't have x as a limit. With this idea in mind, you can make any topological space separable by adding a single point, and making it belong to all open sets. -
Marcos Cossarini
May 5, 2010 at 14:53