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real analysis - Intersection of countable collection of open subsets of a complete metric space can be made complete - Mathematics Stack Exchange
Let's say that [math] \tau [/math] is a topology of X. Then, are all elements of [math] \tau [/math] open sets of X? - Quora
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proof that metrics generate the same topology, if their balls can be contained in one another. - Mathematics Stack Exchange
How does the definition of continuous functions, 'there is always an epsilon neighbourhood of f(a) for every delta neighbourhood of a' (loosely speaking) tell that the functions have gapless graphs? - Quora
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analysis - In $C([0,1],\mathbb{R})$, the sup norm and the $L^1$ norm are not equivalent. - Mathematics Stack Exchange
![general topology - Does it make geometric sense to say that open rectangles and open balls generate the same open sets - Mathematics Stack Exchange general topology - Does it make geometric sense to say that open rectangles and open balls generate the same open sets - Mathematics Stack Exchange](https://i.stack.imgur.com/aWgr6.jpg)
general topology - Does it make geometric sense to say that open rectangles and open balls generate the same open sets - Mathematics Stack Exchange
![Dartmouth Undergraduate Journal of Science - Spring and Summer, 2021 by dartmouthjournalofscience - Issuu Dartmouth Undergraduate Journal of Science - Spring and Summer, 2021 by dartmouthjournalofscience - Issuu](https://image.isu.pub/220106164219-403b88d3e79a1faa1b435b0e86c9376c/jpg/page_1.jpg)
Dartmouth Undergraduate Journal of Science - Spring and Summer, 2021 by dartmouthjournalofscience - Issuu
![general topology - open ball on metric $d''(z,z') = \max \{d_i(x_i,x_i'), i\in \{1,\cdots,n\}\}$ in $\mathbb{R}^2$ - Mathematics Stack Exchange general topology - open ball on metric $d''(z,z') = \max \{d_i(x_i,x_i'), i\in \{1,\cdots,n\}\}$ in $\mathbb{R}^2$ - Mathematics Stack Exchange](https://i.stack.imgur.com/VbUrD.png)
general topology - open ball on metric $d''(z,z') = \max \{d_i(x_i,x_i'), i\in \{1,\cdots,n\}\}$ in $\mathbb{R}^2$ - Mathematics Stack Exchange
![general topology - Is the analogy of neighborhood as open ball applicable to arbitrary topological spaces? - Mathematics Stack Exchange general topology - Is the analogy of neighborhood as open ball applicable to arbitrary topological spaces? - Mathematics Stack Exchange](https://i.stack.imgur.com/fgT5p.jpg)
general topology - Is the analogy of neighborhood as open ball applicable to arbitrary topological spaces? - Mathematics Stack Exchange
![real analysis - Sketch the open ball at the origin $(0,0)$, and radius $1$. - Mathematics Stack Exchange real analysis - Sketch the open ball at the origin $(0,0)$, and radius $1$. - Mathematics Stack Exchange](https://i.stack.imgur.com/j9HN4.jpg)
real analysis - Sketch the open ball at the origin $(0,0)$, and radius $1$. - Mathematics Stack Exchange
![general topology - Does it make geometric sense to say that open rectangles and open balls generate the same open sets - Mathematics Stack Exchange general topology - Does it make geometric sense to say that open rectangles and open balls generate the same open sets - Mathematics Stack Exchange](https://i.stack.imgur.com/A21qU.png)