Recent content by EgoKilla

  1. E

    If p is a covering map with B compact and fiber of b finite, E compact

    I'm honestly so lost.
  2. E

    If p is a covering map with B compact and fiber of b finite, E compact

    Sorry, I'm still confused about why we're even allowed to replace U_\alpha by the V_j at all. We can write p^{-1}(p(V_j)) as a disjoint union of open sets in E, each of which maps homeomorphically to p(V_j). But this must be finite because of the finiteness of the fibers?
  3. E

    If p is a covering map with B compact and fiber of b finite, E compact

    Why are we allowed to replace the U_\alpha by a smaller cover? But then once we have that it's just as simple as saying we can reduce the V_j to a finite subcover since after we map them to B we can take a finite subcover of them and map them back using p^-1 since each open set in the image...
  4. E

    If p is a covering map with B compact and fiber of b finite, E compact

    Homework Statement Let p: E \rightarrow B be a covering map. If B is compact andp^{-1}(b) is finite for each b in B, then E compact. Note: This is a problem from Munkres pg 341, question 6b in section 54. The Attempt at a Solution I begin with a cover of E denote it \{U_\alpha\}. I...