Closure spaces and characterizations of filters in terms of their stone images |
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Authors: | Anh Tran Mynard Frédéric Mynard |
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Institution: | (1) Columbia Law School, 435 West 116th St., New York, NY, 10027;(2) Department of Mathematical Sciences, Georgia Southern University, P. O. BOX 8093, Statesboro, GA, 30460 |
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Abstract: | Fréchet, strongly Fréchet, productively Fréchet, weakly bisequential and bisequential filters (i.e., neighborhood filters
in spaces of the same name) are characterized in a unified manner in terms of their images in the Stone space of ultrafilters.
These characterizations involve closure structures on the set of ultrafilters. The case of productively Fréchet filters answers
a question of S. Dolecki and turns out to be the only one involving a non topological closure structure. |
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Keywords: | filters ultrafilters Frechet closure spaces |
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