Free topological universal algebras and absolute neighborhood retracts

Abstract

We prove that for a complete quasivariety $K$ of topological $E$-algebras of countable discrete signature $E$ and each submetrizable $ANR(k_{\omega })$-space $X$ its free topological $E$-algebra $F_K(X)$ in the class $K$ is a submetrizable $ANR(k_{\omega })$-space.

9 pages

Cited by in corpus (2)

• On rectifiable spaces and its algebraical equivalents, topological algebraic systems and Mal'cev algebras
• On rectifiable spaces and its algebraical equivalents, topological algebraic systems and Mal'cel algebras (continuation)