On the topology of generalized quotients

[EN] 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.Burzyk, J.; Ferens, C.; Mikusinski, P. (2008). On the topology of generalized quotients. Applied General Topology. 9(2):205-212. doi:10.4995/agt.2008.1801.20521292J. 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