On the topology of generalized quotients

Józef Burzyk; Cezary Ferens; Piotr Mikusinski

doi:10.4995/agt.2008.1801

Authors

Józef Burzyk Technical University of Silesia
Cezary Ferens
Piotr Mikusinski University of Central Florida

DOI:

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

Keywords:

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

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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Author Biographies

Józef Burzyk, Technical University of Silesia

Institute of Mathematics

Piotr Mikusinski, University of Central Florida

Department of Mathematics

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.