after the lifting $\tilde f$ of $f$ is defined, the book goes on to prove its continuity. And in that part, the book says that replacing $U$ by a smaller neighborhood, $V_0$ can be contained in $N$. But why is it possible? How to construct a smaller neighborhood such that $V_0$ can be contained i...
I'll repeat the meat of the question here: "And in that part, the book says that replacing $U$ by a smaller neighborhood, $V_0$ can be contained in $N$. But why is it possible? How to construct a smaller neighborhood such that $V_0$ can be contained in $N$?"
The same user then asked this question 8 hours later:
Let $p : E \to B$ be a covering map. And also assume that $B$ is path-connected and locally path-connected. Then, given y in $B$, there exists a neighborhood $U$ of $y_1$ in $B$ that is path-connected and evenly covered by $p$. Now the inverse image of $U$ by $p$ consists of slices $\{V_a\}$. Tak...
I'll also repeat the meat of this question: "Now the questions is, if $N$ is an arbitrary neighborhood of $x$ in $X$, then how to replace $U$ by a smaller neighborhood of $y$ such that the slice $V'$ containing $x$ can be included in the $N$?"
It seems to me a clear case of duplication. However, my flag was rejected. Was I in the wrong?
Hey everyone, I'm new here- hope everyone's having a good day/evening. I'm just really curious behind the meaning of this chatroom's name. What exactly is the topic supposed to be? Just stuff for professionals?
@daOnlyBG this is a room for people who are going to be "executing" or "healing" questions. :)
So, if something needs to be deleted, or flagged, or etc., this is the room for that.
In case anyone ever complains that I delete questions with upvoted answers: math.stackexchange.com/q/433104/23353 I have lost rep because of it, too, and I'm perfectly fine with that.
