THE USE OF FILTERS IN TOPOLOGY

Date Issued:: 2004
Abstract/Description:: Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940).

Title:	THE USE OF FILTERS IN TOPOLOGY.	32 views 16 downloads
Name(s):	Dasser, Abdellatif, Author Richardson, Gary , Committee Chair University of Central Florida, Degree Grantor
Type of Resource:	text
Date Issued:	2004
Publisher:	University of Central Florida
Language(s):	English
Abstract/Description:	Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940).
Identifier:	CFE0000202 (IID), ucf:46271 (fedora)
Note(s):	2004-12-01 M.S. Arts and Sciences, Department of Mathematics Masters This record was generated from author submitted information.
Subject(s):	mathematics topology filters points of closure convergence contnuity compactness
Persistent Link to This Record:	http://purl.flvc.org/ucf/fd/CFE0000202
Restrictions on Access:	public
Host Institution:	UCF

In Collections