Extensions and factorizations of topological and semitopological universal algebras

TL;DR

This paper explores how operations in topological and semitopological universal algebras can be extended to their Stone-ech compactifications and how continuous functions can be factored through homomorphisms to metrizable algebras, focusing on pseudocompact and compact cases.

Contribution

It introduces new methods for extending algebraic operations to compactifications and provides factorization techniques for continuous functions in topological algebra.

Findings

Operations can be extended to Stone-ech compactifications under certain conditions.

Continuous functions can be factored through homomorphisms to metrizable algebras.

Results apply mainly to pseudocompact and compact algebras.

Abstract

The possibility of extending operations of topological and semitopological algebras to their Stone-\v{C}ech compactification and factorization of continuous functions through homomorphisms to metrizable algebras are investigated. Most attention is paid to pseudocompact and compact algebras.