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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That hurt tech stocks. For the past few weeks, the 10-year yield has traded between 1.72% and 2%, as traders moved into the bond for safety when Russia headlines were ugly—and out of it when headlines improved. Now, the yield is touching its pandemic-era high. If the yield breaks above that level, that could signal that it’s on a sustainable path higher. Higher long-dated bond yields make future profits less valuable—and many tech companies are valued on the basis of profits forecast for many years in the future. Right now the digital security needs of Russians and Ukrainians are very different, and they lead to very different caveats about how to mitigate the risks associated with using Telegram. For Ukrainians in Ukraine, whose physical safety is at risk because they are in a war zone, digital security is probably not their highest priority. They may value access to news and communication with their loved ones over making sure that all of their communications are encrypted in such a manner that they are indecipherable to Telegram, its employees, or governments with court orders. Telegram was founded in 2013 by two Russian brothers, Nikolai and Pavel Durov. Crude oil prices edged higher after tumbling on Thursday, when U.S. West Texas intermediate slid back below $110 per barrel after topping as much as $130 a barrel in recent sessions. Still, gas prices at the pump rose to fresh highs. Friday’s performance was part of a larger shift. For the week, the Dow, S&P 500 and Nasdaq fell 2%, 2.9%, and 3.5%, respectively.
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