On Menger algebras
type: Item
instance of: scholarly article
title: On Menger algebras
zbMATH Open document ID: 0603.54016
author: F. A. Gadzhiev
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: A pair (A,\(\phi\) : \(A\times A^ n\to A)\) is called a Menger algebra if \(\phi (\phi (x,Y),Z)=\phi (x,\Phi (Y,Z))\), where \(\Phi =\phi^ n: A^ n\times A^ n\to A^ n\) is the canonical extension of \(\phi\). If X is a topological space, \(A=C(X^ n,X)\) is the seet of continuous maps, \(A^ n\) is identified with \(C(X^ n)\), and \(\phi\) is composition, then \(M(X)=(A,\phi)\) is a Menger algebra. A \(T_ 1\)-space X is admissible, if \(\{f^{\leftarrow}(x): x\in X\), \(f\in C(X)\}\) is a basis for the closed sets. Theorem: Assume that X and Y are admissible, X is doubly homogeneous, and \(| Y| >1\). If there exists an epimorphism \(\eta\) : M(X)\(\to M(Y)\), then X and Y are homeomorphic.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54H10
Mathematics Subject Classification ID: 54H99
zbMATH DE Number: 3973798
zbMATH Keywords: Menger algebras over a topological space
zbMATH Keywords: n-ary Menger algebra
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3973798