Re: Compactness

From: "Saurav" <saurav1111@xxxxxxxxxxxxxx>
Date: 3 Dec 2006 19:58:39 -0800

William Elliot wrote:

A space S is compact iff
every open cover of S has a finite subcover
every filter on S has a cluster point
every ultra filter on S converges.

Well, there is another point:
In a topological space (X,T), a subset A is compact iff for any filter
basis F consisting of closed sets s.t. A clusters F( i.e., A intersects
every member of F), A also cuts the core of F(i.e., /\F).

.

References:
- Compactness
  - From: Saurav
- Re: Compactness
  - From: William Elliot

Prev by Date: odds of 7-10 split in bowling
Next by Date: Re: Compactness
Previous by thread: Re: Compactness
Next by thread: Re: Compactness
Index(es):
- Date
- Thread

Relevant Pages

Re: Access 2000 ADP - error when applying form filter - error message "The column prefix XXX do
... maybe it is the caracter # in the Cluster# that gives DAP a hiccup. ... with DAP; even if they are perfectly valid under T-SQL. ... you don't give us what is the form filter that you are using and how ... > name used in the query" ...
(microsoft.public.sqlserver.odbc)
Re: Access 2000 ADP - error when applying form filter - error message "The column prefix XXX do
... maybe it is the caracter # in the Cluster# that gives DAP a hiccup. ... with DAP; even if they are perfectly valid under T-SQL. ... you don't give us what is the form filter that you are using and how ... > name used in the query" ...
(microsoft.public.access.forms)
Re: IPSec and clusters Easy Read Filters
... supports IPsec on WS03 clusters so we are sailing into new waters here. ... Filter Action: Allow ... > After one or both cluster nodes are rebooted the "filter ... > Destination Port Source DNS Source Address ...
(microsoft.public.win2000.security)
cluster question
... I have a cluster (3.1, solaris 9) with applications running on node 1 ... A uses udp port x, ... packet filter. ...
(comp.unix.solaris)