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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/10829

Title: category of lattice-valued Preuss filter groups and its related categories
Authors: . Ahsanullah, T. M. G
Keywords: ; G. Preuss
G. Jager
Issue Date: 2010
Publisher: Topology conference
Citation: , July 25-30, 2010
Abstract: By dropping one of the axioms of stratified lattice-valued Cauchy space recently introduced by G. Jager [Lattice-valued Cauchy spaces and completion, Quaest. Math. 33(2010), 53-74], we name the resulting space a stratified lattice-valued filter space - a generalization of Preuss filter space attributted to G. Preuss [Foundadtions of Topology: An Approach to Convenient Topology, Kluwer Academic Publishers, Dordrecht, 2002]. Denoting S$L$-Fil, the category of stratified lattice-valued filter spaces, we show that the category of stratified lattice-valued Cauchy spaces and Cauchy continuous maps, S$L$-Chy, is a refective subcategory of S$L$-Fil. Presenting the notion of stratified lattice-valued semiuniform convergence space, we show that the category of stratified lattice-valued filter-determined stratified lattice-valued semiuniform convergence spaces, S$L$Fil-D-S$L$-SUConv, is isomorphic to the category of stratified lattice-valued filter spaces, S$L$-Fil. We introduce among others, the category of stratified lattice-valued filter groups, S$L$-FilGrp, stratified lattice-valued semiuniform convergence groups, S$L$-SUConvGrp, and stratified lattice-valued semiuniform limit groups, S$L$-SULimGrp. In some of these categories, we look into the impact on objects and morphisms from categorical point of view when the underlying basis lattices are changed under so called functorial mechanism employed by U. Hohle and A. P. Sostak [Axiomatics foundations of fixed basis fuzzy topology, in: Mathematics of Fuzzy Sets: Topology, Logic and Measure Theory, Edited by U. Hohle and S. E. Rodabaugh, Kluwer Academic Publishers, Dordrecht, 1999] for lattice-valued topologies and lattice-valued fuzzy topologies; later studied by G. Jager in [Subcategories of lattice-valued convergence spaces, International J. Fuzzy Sets and Systems 156(2005), 1-24] for stratified convergence spaces, and by T. M. G. Ahsanullah and Fawzi Al-Thukair in [Change of basis for lattice-valued convergence groups, New Math. and Natural Computation, World Scientific Publishing, to appear] for stratified lattice-valued convergence groups. Some connections are made between various categories achieved in [T. M. G. Ahsanullah, Lattice-valued convergence ring and its uniform convergence structure, Quaest. Math. 33(2010), 21-51], and the present text.
URI: http://hdl.handle.net/123456789/10829
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