NEW YORK SEMINAR ON GENERAL TOPOLOGY AND TOPOLOGICAL ALGEBRA

October - December 2014

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OCTOBER 16:   Frederic Mynard, New Jersey City University, will discuss "Pointfree convergence". At CCNY; tea 3:15pm NAC 8/130, talk 4pm SH 205. For more information, contact Ralph Kopperman, rdkcc@ccny.cuny.edu.

     ABSTRACT:   This is a preliminary report on joint work with Jean Goubault-Larrecq. To investigate pointfree convergence, a pointfree analog of the theory of convergence spaces, we introduce the category of convergence lattices and its opposite category Foc of focales. Let Conv denote the category of convergence spaces and continuous maps. Each convergence space determines a focal via a functor L:Conv -> Foc, and each focal determines a convergence space on its set of points via a functor pt:Foc -> Conv.

      We show that L -| pt is an adjunction between Conv and Foc, and we characterize the image of pt in Conv, and investigate the fixed points of ptL, among which are in particular T0 sober topological spaces. We further examine the relationship between this duality and the traditional Stone duality between the categories of topological spaces and of locales.

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For more information, contact:

CCNY ): R. Kopperman (845-915-0914), S. Popvassilev (212-650-5346)
College of Staten Island (718-982-3626): P. R. Misra
Baruch College (646-312-4136): A. Todd
LIU C. W. Post Center (516-299-2447): S. Andima
Medgar Evers College, (718-270-6416): H. Pajoohesh
Queensborough Community College, (718-281-5291): F. Jordan