Boustique, H.; Mikusinski, Piotr; Richardson, Gary(Universitat Politècnica de València, 2009-10-01)
[EN] Continuous actions of a convergence semigroup are investigated in the category of convergence spaces. Invariance properties of actions as well as properties of a generalized quotient space are presented
Richardson, Gary; Mikusinski, Piotr; Boustique, H.(Universitat Politècnica de València, 2010-10-01)
[EN] Properties of the category consisting of all objects of the form (X, S, λ) are investigated, where X is a convergence space, S is a commutative semigroup, and λ: X × S → X is a continuous action. A “generalized quotient” ...
Burzyk, Józef; Ferens, Cezary; Mikusinski, Piotr(Universitat Politècnica de València, 2008-10-01)
[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 ...