Keywords

mathematics, topology, filters, points of closure, convergence, contnuity, compactness

Abstract

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).

Notes

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Graduation Date

2004

Semester

Fall

Advisor

Richardson, Gary

Degree

Master of Science (M.S.)

College

College of Arts and Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0000202

URL

http://purl.fcla.edu/fcla/etd/CFE0000202

Language

English

Release Date

December 2004

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

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Included in

Mathematics Commons

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