On the topology of generalized quotients
DOI:
https://doi.org/10.4995/agt.2008.1801Keywords:
Generalized quotients, Semigroup acting on a set, Quotient topology, Hausdorff topologyAbstract
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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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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