On the topology of generalized quotients

Józef Burzyk

Poland

Technical University of Silesia

Institute of Mathematics

Cezary Ferens

Poland

Piotr Mikusinski

United States

University of Central Florida

Department of Mathematics

Submitted: 2013-10-30

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Accepted:

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DOI: https://doi.org/10.4995/agt.2008.1801
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Keywords:

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

Supporting agencies:

This research was not funded

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.

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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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