On the topology of generalized quotients


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




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


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


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.


How to Cite

J. Burzyk, C. Ferens, and P. Mikusinski, “On the topology of generalized quotients”, Appl. Gen. Topol., vol. 9, no. 2, pp. 205–212, Oct. 2008.



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