Упражнение: докажите, что любую поверхность (компактную связную без края) можно получить из сферы последовательностью раздутий и сдутий.
«Топологическая гипотеза Нэша», доказанная Г.Михалкиным: аналогичное утверждение верно в любой размерности — любое вещественное многообразие (гладкое компактное связное без края) можно превратить в любое другое последовательностью раздутий и сдутий вдоль подмногообразий.
Упражнение: докажите, что любую поверхность (компактную связную без края) можно получить из сферы последовательностью раздутий и сдутий.
«Топологическая гипотеза Нэша», доказанная Г.Михалкиным: аналогичное утверждение верно в любой размерности — любое вещественное многообразие (гладкое компактное связное без края) можно превратить в любое другое последовательностью раздутий и сдутий вдоль подмногообразий.
// via ppetya
BY Непрерывное математическое образование
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The fake Zelenskiy account reached 20,000 followers on Telegram before it was shut down, a remedial action that experts say is all too rare. "Russians are really disconnected from the reality of what happening to their country," Andrey said. "So Telegram has become essential for understanding what's going on to the Russian-speaking world." "There are a lot of things that Telegram could have been doing this whole time. And they know exactly what they are and they've chosen not to do them. That's why I don't trust them," she said. What distinguishes the app from competitors is its use of what's known as channels: Public or private feeds of photos and videos that can be set up by one person or an organization. The channels have become popular with on-the-ground journalists, aid workers and Ukrainian President Volodymyr Zelenskyy, who broadcasts on a Telegram channel. The channels can be followed by an unlimited number of people. Unlike Facebook, Twitter and other popular social networks, there is no advertising on Telegram and the flow of information is not driven by an algorithm. Channels are not fully encrypted, end-to-end. All communications on a Telegram channel can be seen by anyone on the channel and are also visible to Telegram. Telegram may be asked by a government to hand over the communications from a channel. Telegram has a history of standing up to Russian government requests for data, but how comfortable you are relying on that history to predict future behavior is up to you. Because Telegram has this data, it may also be stolen by hackers or leaked by an internal employee.
from kr
