mathematics, topology, filters, points of closure, convergence, contnuity, compactness
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).
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Master of Science (M.S.)
College of Arts and Sciences
Length of Campus-only Access
Masters Thesis (Open Access)
Dasser, Abdellatif, "The Use Of Filters In Topology" (2004). Electronic Theses and Dissertations, 2004-2019. 177.