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JOURNALS // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Archive

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011 Number 1, Pages 50–59 (Mi basm279)

Research articles

Free topological universal algebras and absolute neighborhood retracts

Taras Banakhab, Olena Hryniva

a Ivan Franko National University of Lviv, Ukraine
b Jan Kochanowski University in Kielce, Poland

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

Keywords and phrases: topological universal algebra, free topological universal algebra, a quasivariety of topological algebras, absolute neighborhood retract, absolute neighborhood extensor, $k_\omega$-space.

MSC: 08B20, 22A30, 54C55

Received: 06.04.2010

Language: English



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