On the topology of generalized quotients

Józef Burzyk, Cezary Ferens, Piotr Mikusinski

Abstract

Generalized quotients are defined as equivalence classes of pairs (x, f), where x is an element of a nonempty set X and f is an element of a commutative semigroup G acting on X. Topologies on X and G induce a natural topology on B(X,G), the space of generalized quotients. Separation properties of this topology are investigated.


Keywords

Generalized quotients; Semigroup acting on a set; Quotient topology; Hausdorff topology

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References

D. Bradshaw, M. Khosravi, H. M. Martin and P. Mikusinski, On Categorical and Topological Properties of Generalized Quotients, preprint.

J. Burzyk and P. Mikusinski, A generalization of the construction of a field of quotients with applications in analysis, Int. J. Math. Sci. 2 (2003), 229–236.

J. H. Carruth, J. A. Hildebrant, and R. J. Koch, The Theory of Topological Semigroups (Marcel Dekker, New York, 1983).

P. Mikusinski, Generalized Quotients with Applications in Analysis, Methods Appl. Anal. 10 (2004), 377–386.

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1. Convergence semigroup actions: generalized quotients
H. Boustique, Piotr Mikusinski, Gary Richardson
Applied General Topology  vol: 10  issue: 2  first page: 173  year: 2009  
doi: 10.4995/agt.2009.1731



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt