Convergence semigroup categories

Gary Richardson

United States

University of Central Florida

H. Boustique

United States

University of Central Florida

Piotr Mikusinski

United States

University of Central Florida

Submitted: 2013-09-24

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Accepted: 2013-09-24

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Published: 2013-09-24

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

Convergence space, Convergence semigroup, Ccontinuous action, Categorical properties

Supporting agencies:

This research was not funded

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