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I'm deeply impressed by mathematics.


3h
accepted Show that $S=\mathbb R^2\setminus\{(a,b):a,b\in\mathbb Q\}$ is path connected.
5h
asked Show that $S=\mathbb R^2\setminus\{(a,b):a,b\in\mathbb Q\}$ is path connected.
5h
accepted Prove that intersection of connected spaces is connceted.
5h
accepted Prove that regular $T_1$ space is $T_2$ space.
6h
accepted Show that $\frac{\Gamma(\frac 1 3)^2}{\Gamma(\frac 1 6)}=\frac{\sqrt {\pi}\sqrt[3] 2}{\sqrt 3}$.
19h
asked Show that $\frac{\Gamma(\frac 1 3)^2}{\Gamma(\frac 1 6)}=\frac{\sqrt {\pi}\sqrt[3] 2}{\sqrt 3}$.
1d
accepted Show that T2-space is preserved by continuous map.
1d
asked Show that T2-space is preserved by continuous map.
1d
comment Show that a map f : (X,$\tau$) $\rightarrow$ (Y,$\tau_1$) is continuous if and only if $f^{-1}(U)\in\tau$ , for every $U\in$B1
Haha, I know what I was doing wrong. Thanks.
1d
accepted Show that a map f : (X,$\tau$) $\rightarrow$ (Y,$\tau_1$) is continuous if and only if $f^{-1}(U)\in\tau$ , for every $U\in$B1
1d
comment Show that a map f : (X,$\tau$) $\rightarrow$ (Y,$\tau_1$) is continuous if and only if $f^{-1}(U)\in\tau$ , for every $U\in$B1
But I still can't conclude $f^{-1} (U)\in\tau$.
1d
accepted Show that $\int^\infty_0\left(\frac{\ln(1+x)} x\right)^2dx$ converge.
1d
comment Show that $\int^\infty_0\left(\frac{\ln(1+x)} x\right)^2dx$ converge.
Sorry, I mean the second equation.
2d
comment Show that $\int^\infty_0\left(\frac{\ln(1+x)} x\right)^2dx$ converge.
Can you please explain the third equation a bit?
2d
asked Show that $\int^\infty_0\left(\frac{\ln(1+x)} x\right)^2dx$ converge.
2d
comment Show that a map f : (X,$\tau$) $\rightarrow$ (Y,$\tau_1$) is continuous if and only if $f^{-1}(U)\in\tau$ , for every $U\in$B1
Ya, $f^{-1}(V)\in\tau$, $f^{-1}(\cup U_i)\in\tau$, then $\cup f^{-1}(U_i)\in\tau$.
2d
comment Show that a map f : (X,$\tau$) $\rightarrow$ (Y,$\tau_1$) is continuous if and only if $f^{-1}(U)\in\tau$ , for every $U\in$B1
Let $V\in\tau_1,V=\cup U_i$. Then $\cup f^{-1} (U_i)\in\tau$, right? I can't see how I can proceed to $f^{-1} (U_i)\in\tau$...
2d
asked Show that a map f : (X,$\tau$) $\rightarrow$ (Y,$\tau_1$) is continuous if and only if $f^{-1}(U)\in\tau$ , for every $U\in$B1
Jul
26
comment Fun Geometric Series Puzzle
I can't believe how complicated will the solution of your generalized problem be without using complex approach.
Jul
25
revised Prove that regular $T_1$ space is $T_2$ space.
added 4 characters in body