Extending binary operations to funtor-spaces

TL;DR

This paper presents a method to extend semigroup operations from discrete topological semigroups to their functor-spaces within Tychonov spaces, ensuring the extended operation is right-topological with a dense subsemigroup of finite support elements.

Contribution

It introduces a way to extend binary operations to functor-spaces in Tychonov spaces, preserving topological and algebraic properties.

Findings

Extended semigroup operation is right-topological.

The topological center includes a dense subsemigroup of finite support elements.

The extension maintains the algebraic structure within the functor-space.

Abstract

Given a continuous monadic functor T in the category of Tychonov spaces for each discrete topological semigroup X we extend the semigroup operation of X to a right-topological semigroup operation on TX whose topological center contains the dense subsemigroup of all elements of TX that have finite support.