-
Notifications
You must be signed in to change notification settings - Fork 24
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
10 changed files
with
37 additions
and
42 deletions.
There are no files selected for viewing
This file was deleted.
Oops, something went wrong.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,14 @@ | ||
--- | ||
space: S000131 | ||
property: P000183 | ||
value: true | ||
refs: | ||
- mathse: 4844426 | ||
name: Answer to "Can a Fréchet-Urysohn hemicompact Hausdorff space fail to be locally compact?" | ||
--- | ||
|
||
Each spine $C_m=(\{m\}\times\omega)\cup\{\infty\}$ is a closed subspace of $X$ homeomorphic to a convergent sequence ({S20}); | ||
and {S20|P183}. | ||
And every compact subset of $X$ is contained in the union of a finite number of these spines. | ||
|
||
Therefore, taking a countable $k$-network from each of the (countably many) spines and forming their union gives a countable $k$-network for $X.$ |
This file was deleted.
Oops, something went wrong.
This file was deleted.
Oops, something went wrong.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,10 @@ | ||
--- | ||
space: S000139 | ||
property: P000183 | ||
value: true | ||
--- | ||
|
||
Each of the circles (corresponding to an interval $[n,n+1]$, $n\in\mathbb Z$, with the endpoints identified) is a closed subspace of $X$ and {S170|P183}. | ||
And every compact subset of $X$ is contained in the union of a finite number of these circles. | ||
|
||
Therefore, taking a countable $k$-network from each of the (countably many) circles and forming their union gives a countable $k$-network for $X.$ |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file was deleted.
Oops, something went wrong.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,10 @@ | ||
--- | ||
space: S000156 | ||
property: P000183 | ||
value: true | ||
refs: | ||
- mathse: 4673444 | ||
name: Answer to "Is the Arens space hemicompact but not locally compact?" | ||
--- | ||
|
||
See the last part of {{mathse:4673444}}. |