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
![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 - "The closure of the unit ball of $C^1[0, 1]$ in $C[0, 1]$" and its compactness - Mathematics Stack Exchange general topology - "The closure of the unit ball of $C^1[0, 1]$ in $C[0, 1]$" and its compactness - Mathematics Stack Exchange](https://i.stack.imgur.com/Bp0CC.jpg)
general topology - "The closure of the unit ball of $C^1[0, 1]$ in $C[0, 1]$" and its compactness - Mathematics Stack Exchange
![real analysis - Showing that open subsets for two metrics of same space coincide. - Mathematics Stack Exchange real analysis - Showing that open subsets for two metrics of same space coincide. - Mathematics Stack Exchange](https://i.stack.imgur.com/C1fJi.png)
real analysis - Showing that open subsets for two metrics of same space coincide. - Mathematics Stack Exchange
![analysis - In $C([0,1],\mathbb{R})$, the sup norm and the $L^1$ norm are not equivalent. - Mathematics Stack Exchange analysis - In $C([0,1],\mathbb{R})$, the sup norm and the $L^1$ norm are not equivalent. - Mathematics Stack Exchange](https://i.stack.imgur.com/PwslL.png)
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/A21qU.png)
general topology - Does it make geometric sense to say that open rectangles and open balls generate the same open sets - Mathematics Stack Exchange
![proof that metrics generate the same topology, if their balls can be contained in one another. - Mathematics Stack Exchange proof that metrics generate the same topology, if their balls can be contained in one another. - Mathematics Stack Exchange](https://i.stack.imgur.com/GBeBD.png)
proof that metrics generate the same topology, if their balls can be contained in one another. - 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
![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)