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fabricebaudoin.blog | ||
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thehighergeometer.wordpress.com
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| | | | | Here's a fun thing: if you want to generate a random finite $latex T_0$ space, instead select a random subset from $latex \mathbb{S}^n$, the $latex n$-fold power of the Sierpinski space $latex \mathbb{S}$, since every $latex T_0$ space embeds into some (arbitrary) product of copies of the Sierpinski space. (Recall that $latex \mathbb{S}$ has underlying... | |
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pfzhang.wordpress.com
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| | | | | Consider a smooth one-parameter family $latex {f_t}$ of diffeomorphisms on a manifold $latex M$. It is a flow if $latex f_0(x)=x$ and $latex f_{t}\circ f_{s}(x) = f_{s+t}(x)$ for every $latex x\in M$, , $latex t ,s \in \mathbb{R}$. Set $latex X(x)=\lim\limits_{h\to 0} \frac{1}{h}(f_h(x) - x)$. This generates a vector field $latex X: M \to TM$.... | |
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dominiczypen.wordpress.com
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| | | | | Let $latex \omega$ denote the first infinite cardinal - that is, the set of non-negative integers. Let $latex p_0 = 2$ be the smallest prime number, and let $latex (p_n)_{n\in\omega}$ enumerate all prime numbers in ascending order. Let $latex \mathcal{U}$ be a free ultrafilter on $latex \omega$. We consider the field $latex F = \big(\prod_{n\in\omega}\mathbb{Z}/p_n\mathbb{Z}\big)/{\mathcal... | |
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cambridge163.wordpress.com
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| | | This is the excerpt for your very firstpost. | ||
