![SOLVED: Prove that locally compact; Hausdorff space X Is locally compact iff its of the (orm Unr for some open set Uand closed set in X SOLVED: Prove that locally compact; Hausdorff space X Is locally compact iff its of the (orm Unr for some open set Uand closed set in X](https://cdn.numerade.com/project-universal/previews/61dee5da-8269-46b3-b24c-20c3d4fce989.gif)
SOLVED: Prove that locally compact; Hausdorff space X Is locally compact iff its of the (orm Unr for some open set Uand closed set in X
![fa.functional analysis - A question on the Riesz-Markov theorem about dual space of $C_0(X)$ - MathOverflow fa.functional analysis - A question on the Riesz-Markov theorem about dual space of $C_0(X)$ - MathOverflow](https://i.stack.imgur.com/fZHo9.png)
fa.functional analysis - A question on the Riesz-Markov theorem about dual space of $C_0(X)$ - MathOverflow
![general topology - locally compact, Hausdorff, second-countable $\Rightarrow$ paracompact - Mathematics Stack Exchange general topology - locally compact, Hausdorff, second-countable $\Rightarrow$ paracompact - Mathematics Stack Exchange](https://i.stack.imgur.com/P32Lc.png)
general topology - locally compact, Hausdorff, second-countable $\Rightarrow$ paracompact - Mathematics Stack Exchange
![SOLVED: Texts: Let E be a locally compact Hausdorff space. Prove that: (a) If dim E < ∞, then E is locally compact. (b) Now we assume that E is locally compact. SOLVED: Texts: Let E be a locally compact Hausdorff space. Prove that: (a) If dim E < ∞, then E is locally compact. (b) Now we assume that E is locally compact.](https://cdn.numerade.com/ask_images/01fb4e4cb5f04e00b515e49d121cd6fd.jpg)
SOLVED: Texts: Let E be a locally compact Hausdorff space. Prove that: (a) If dim E < ∞, then E is locally compact. (b) Now we assume that E is locally compact.
![general topology - Is a compactly supported function on a locally compact Hausdorff space uniformly continuous? - Mathematics Stack Exchange general topology - Is a compactly supported function on a locally compact Hausdorff space uniformly continuous? - Mathematics Stack Exchange](https://i.stack.imgur.com/QqRxE.png)
general topology - Is a compactly supported function on a locally compact Hausdorff space uniformly continuous? - 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: Texts: Let E be a locally compact Hausdorff space. F is a finite dimensional subspace of E. (a) Make x ∈ E/F. Prove: There exists a continuous seminorm p on E SOLVED: Texts: Let E be a locally compact Hausdorff space. F is a finite dimensional subspace of E. (a) Make x ∈ E/F. Prove: There exists a continuous seminorm p on E](https://cdn.numerade.com/ask_images/5a3a8470a9154ec7af1ae2d10d80104e.jpg)
SOLVED: Texts: Let E be a locally compact Hausdorff space. F is a finite dimensional subspace of E. (a) Make x ∈ E/F. Prove: There exists a continuous seminorm p on E
![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 - 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
![general topology - Is it always possible to extend continuous functions defined on a *closed* subset of a locally compact Hausdorff space? - Mathematics Stack Exchange general topology - Is it always possible to extend continuous functions defined on a *closed* subset of a locally compact Hausdorff space? - Mathematics Stack Exchange](https://i.stack.imgur.com/qa6pq.png)
general topology - Is it always possible to extend continuous functions defined on a *closed* subset of a locally compact Hausdorff space? - Mathematics Stack Exchange
![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/y7EpC.png)