Convergence semigroup categories

Gary Richardson; H. Boustique; Piotr Mikusinski

doi:10.4995/agt.2010.1709

Authors

Gary Richardson University of Central Florida
H. Boustique University of Central Florida
Piotr Mikusinski University of Central Florida

DOI:

https://doi.org/10.4995/agt.2010.1709

Keywords:

Convergence space, Convergence semigroup, Ccontinuous action, Categorical properties

Abstract

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 â†’ X is a continuous action. A “generalized quotient” of each object is defined without making the usual assumption that for each fixed g âˆˆ S, λ(., g) : X â†’ X is an injection.

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