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Apr
10
asked Separation of variables for a non homogeneous PDE $u_t-ku_{xx} = f(x,t),\quad u(0,t)=u(L,t)=0,\quad u(x,0)=\phi(x)$
Apr
2
accepted (Proof Checking) Prove that if $C,C'$ are compact subsets of a hausdorff space $X$ then $C\cap C'$ is compact in $X$.
Apr
2
comment (Proof Checking) Prove that if $C,C'$ are compact subsets of a hausdorff space $X$ then $C\cap C'$ is compact in $X$.
@k.stm You are right, thanks for clearing up the confusion!
Apr
2
asked (Proof Checking) Prove that if $C,C'$ are compact subsets of a hausdorff space $X$ then $C\cap C'$ is compact in $X$.
Apr
2
comment find a sequence of closed connected subsets $V_n$ of $\mathbb R^2$ s.t. $V_n\supseteq V_{n+1}$ and $\cap^{\infty}_{i=1}V_i$ is not connected
Ah great, I understand now. Thanks, that's also a nice example!
Apr
2
comment find a sequence of closed connected subsets $V_n$ of $\mathbb R^2$ s.t. $V_n\supseteq V_{n+1}$ and $\cap^{\infty}_{i=1}V_i$ is not connected
Thanks a lot, that's a nice example. @Andre Caldas, If I understand correctly, wouldn't you end up with an the empty set if you take the infinite intersection?
Apr
2
accepted find a sequence of closed connected subsets $V_n$ of $\mathbb R^2$ s.t. $V_n\supseteq V_{n+1}$ and $\cap^{\infty}_{i=1}V_i$ is not connected
Apr
2
comment find a sequence of closed connected subsets $V_n$ of $\mathbb R^2$ s.t. $V_n\supseteq V_{n+1}$ and $\cap^{\infty}_{i=1}V_i$ is not connected
@nik Thanks for your answer. So we would have something like $V_n = \{ (x,y)\in \mathbb R^n: |x| \geq 1 \}\cup \{ (x,y) \in \mathbb R^2 : |x| \leq 1, y\geq n \}$? The first set being the two closed sides of the plane and the last set being the bridge?
Apr
2
asked find a sequence of closed connected subsets $V_n$ of $\mathbb R^2$ s.t. $V_n\supseteq V_{n+1}$ and $\cap^{\infty}_{i=1}V_i$ is not connected
Mar
11
comment Solving integral including a triangle
Well in the picture you linked the integral is from $0$ to $4$ so the domain of integration does not include the triangle. It it simply the area of a half circle of radius $2$. Unless I am missing something.
Feb
13
comment If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
Thanks, that's a nice approach. I wonder if anyone actually read the mess I wrote haha. Thanks for the answer!
Feb
13
accepted If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
Feb
13
comment If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
Ah this is great, actually the first part of this question asked us to show this for real numbers, can't believe I didn't manage to see the connection. Thanks a lot!
Feb
13
comment $f:X\to Y$, $A,B,\subseteq X$. Show that $f(A\setminus B)=f(A)\setminus f(B)$ iff $f(A\setminus B)\cap f(B) =\emptyset$
Thanks for the answer! :)
Feb
13
comment $f:X\to Y$, $A,B,\subseteq X$. Show that $f(A\setminus B)=f(A)\setminus f(B)$ iff $f(A\setminus B)\cap f(B) =\emptyset$
Thanks a lot, your way of showing the first part is indeed a lot clearer than what I had.
Feb
13
accepted $f:X\to Y$, $A,B,\subseteq X$. Show that $f(A\setminus B)=f(A)\setminus f(B)$ iff $f(A\setminus B)\cap f(B) =\emptyset$
Feb
13
asked If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
Feb
11
asked Solve $yu_x+xu_y=0$ where $u(0,y)=\exp(-y^2)$. Where in the $xy$-plane is the solution uniquely determined?
Feb
10
revised $f:X\to Y$, $A,B,\subseteq X$. Show that $f(A\setminus B)=f(A)\setminus f(B)$ iff $f(A\setminus B)\cap f(B) =\emptyset$
edited body
Feb
10
asked $f:X\to Y$, $A,B,\subseteq X$. Show that $f(A\setminus B)=f(A)\setminus f(B)$ iff $f(A\setminus B)\cap f(B) =\emptyset$