![SOLVED: Problem 3: (15 points + 10 points) Suppose that X and Y are locally compact (but not compact) Hausdorff spaces with one-point compactifications Xo and Yo respectively: Further suppose that (X Y) SOLVED: Problem 3: (15 points + 10 points) Suppose that X and Y are locally compact (but not compact) Hausdorff spaces with one-point compactifications Xo and Yo respectively: Further suppose that (X Y)](https://cdn.numerade.com/ask_images/c219b6bcc57e472cbcf4d05bba9568d7.jpg)
SOLVED: Problem 3: (15 points + 10 points) Suppose that X and Y are locally compact (but not compact) Hausdorff spaces with one-point compactifications Xo and Yo respectively: Further suppose that (X Y)
![SOLVED: Problem 3: A topological space X is locally compact if every € € X has neighborhood N which is compact. Show: Ed is locally compact; 2 If X is locally compact SOLVED: Problem 3: A topological space X is locally compact if every € € X has neighborhood N which is compact. Show: Ed is locally compact; 2 If X is locally compact](https://cdn.numerade.com/ask_images/86acb69cf3734800a626f1e2719386f8.jpg)
SOLVED: Problem 3: A topological space X is locally compact if every € € X has neighborhood N which is compact. Show: Ed is locally compact; 2 If X is locally compact
![real analysis - Can every continuous function be extended from a locally compact Hausdorff space to the one-point compactification? - Mathematics Stack Exchange real analysis - Can every continuous function be extended from a locally compact Hausdorff space to the one-point compactification? - Mathematics Stack Exchange](https://i.stack.imgur.com/aSr08.png)