Category:Strongly Locally Compact Spaces

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This category contains results about Strongly Locally Compact Spaces.

Let $T = \left({S, \tau}\right)$ be a topological space.

Definition 1

The space $T$ is strongly locally compact if and only if:

every point of $S$ is contained in an open set whose closure is compact.

Definition 2

The space $T$ is strongly locally compact if and only if:

every point has a closed compact neighborhood.

That is:

every point of $S$ is contained in an open set which is contained in a closed compact subspace.

Subcategories

This category has only the following subcategory.

E

Existence of Weakly Locally Compact Space which is not Strongly Locally Compact‎ (3 P)

Pages in category "Strongly Locally Compact Spaces"

The following 9 pages are in this category, out of 9 total.

C

Compact Space is Strongly Locally Compact

D

Discrete Space is Strongly Locally Compact

E

I

Infinite Particular Point Space is not Strongly Locally Compact

M

Metric Space is Weakly Locally Compact iff Strongly Locally Compact

S

Strongly Locally Compact Space is Weakly Locally Compact

W

Weakly Locally Compact Hausdorff Space is Strongly Locally Compact

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Compact Spaces