![real analysis - Baire category theorem for locally compact and Hausdorff proof - Mathematics Stack Exchange real analysis - Baire category theorem for locally compact and Hausdorff proof - Mathematics Stack Exchange](https://i.stack.imgur.com/vYOxH.png)
real analysis - Baire category theorem for locally compact and Hausdorff proof - Mathematics Stack Exchange
![general topology - Compact Hausdorff Spaces and their local compactness - Mathematics Stack Exchange general topology - Compact Hausdorff Spaces and their local compactness - Mathematics Stack Exchange](https://i.stack.imgur.com/SQgWz.jpg)
general topology - Compact Hausdorff Spaces and their local compactness - Mathematics Stack Exchange
![SOLVED: Let X be a locally compact, normal, Hausdorff space (or take K to be the real numbers if you wish). Let Cc(X) denote the set of continuous functions on X with SOLVED: Let X be a locally compact, normal, Hausdorff space (or take K to be the real numbers if you wish). Let Cc(X) denote the set of continuous functions on X with](https://cdn.numerade.com/ask_images/1efd87b464c84de78c28ffe65fac5e76.jpg)
SOLVED: Let X be a locally compact, normal, Hausdorff space (or take K to be the real numbers if you wish). Let Cc(X) denote the set of continuous functions on X with
![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)
![general topology - Does locally compact separable Hausdorff imply $\sigma$- compact? - Mathematics Stack Exchange general topology - Does locally compact separable Hausdorff imply $\sigma$- compact? - Mathematics Stack Exchange](https://i.stack.imgur.com/qZUuT.png)
general topology - Does locally compact separable Hausdorff imply $\sigma$- compact? - Mathematics Stack Exchange
![general topology - For the existence of one-point compactification, do we need locally compactness? - Mathematics Stack Exchange general topology - For the existence of one-point compactification, do we need locally compactness? - Mathematics Stack Exchange](https://i.stack.imgur.com/vm4Q8.png)
general topology - For the existence of one-point compactification, do we need locally compactness? - Mathematics Stack Exchange
![SOLVED: Problem 5.a Let C be a closed subspace of a compact Hausdorff space. Show that E/C is homeomorphic to the one-point compactification of E-C. (b) If A and B are spaces SOLVED: Problem 5.a Let C be a closed subspace of a compact Hausdorff space. Show that E/C is homeomorphic to the one-point compactification of E-C. (b) If A and B are spaces](https://cdn.numerade.com/ask_images/fc5beae5bb1048838c9a79837b7f5569.jpg)
SOLVED: Problem 5.a Let C be a closed subspace of a compact Hausdorff space. Show that E/C is homeomorphic to the one-point compactification of E-C. (b) If A and B are spaces
![general topology - Quasicomponents and components in compact Hausdorff space - Mathematics Stack Exchange general topology - Quasicomponents and components in compact Hausdorff space - Mathematics Stack Exchange](https://i.stack.imgur.com/BTi0B.png)
general topology - Quasicomponents and components in compact Hausdorff space - 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 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)