Add to ORKGA space X is Mal'tsev if there exists a continuous map M: X3 → X such that M(x, y, y) = x = M(y, y, x). A space X is retral if it is a retract of a topological group. Every retral space is Mal'tsev. General methods for constructing Mal'tsev and retral spaces are given. An example of a Mal'tsev space which is not retral is presented. An example of a Lindelöf topological group with cellularity the continuum is presented. Constraints on the examples are examined.Copyright 1997 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0
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An S-space is any topological space which is hereditarily separable but not Lindelof. An L-space, on...
A space X is Mal'tsev if there exists a continuous map M: X3 → X such that M(x, y, y) = x ...
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AbstractWe prove a Dichotomy Theorem: for any Hausdorff compactification bG of an arbitrary rectifia...
summary:We prove a Dichotomy Theorem: for each Hausdorff compactification $bG$ of an arbitrary topol...
An S-space is any topological space which is hereditarily separable but not Lindelof. An L-space, on...
A space X is Mal'tsev if there exists a continuous map M: X3 → X such that M(x, y, y) = x ...
AbstractA space X is Mal'tsev if there exists a continuous map M : X3 → X such that M(x, y, y) = x =...
AbstractThe paper presents some recent results on the topics in its title, in the context of an ongo...
AbstractA theorem due to Comfort and Ross asserts that the product of any family of pseudocompact to...
summary:We show that every retral continuum with the fixed point property is locally connected. It f...
summary:We consider $M$-mappings which include continuous mappings of spaces onto topological groups...
AbstractApplying the continuum hypothesis, we construct a hereditarily separable and hereditarily no...
The word “Mathematics” comes from Greek word “Mathema” which means science, knowledge or learning; m...
AbstractThe notions of the relative cellularity (≡ relative Souslin number) c(X,Y) and the relative ...
In this paper, we s~all prove that an Ml-space X can be imbedded in an Ml-space Z(X) as a closed sub...
In many natural objects of topological algebra that possess the algebraic structure of a group, the ...
AbstractWe show that every Hausdorff topological group is a group retract of a minimal topological g...
AbstractWe prove a Dichotomy Theorem: for any Hausdorff compactification bG of an arbitrary rectifia...
summary:We prove a Dichotomy Theorem: for each Hausdorff compactification $bG$ of an arbitrary topol...
An S-space is any topological space which is hereditarily separable but not Lindelof. An L-space, on...