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Mal'tsev and retral spaces

Abstract:
A 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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Institution:
University of Oxford
Oxford college:
St Edmund Hall
Department:
Mathematical,Physical & Life Sciences Division - Mathematical Institute
Role:
Author
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Institution:
Moscow State University
Role:
Author
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Institution:
Moscow State University
Role:
Author
Publisher:
Elsevier Inc. Publisher's website
Journal:
Topology and its Applications Journal website
Volume:
80
Issue:
1-2
Pages:
115–129
Publication date:
1997-10-05
ISSN:
0166-8641
URN:
uuid:7c6d39b2-4818-43a4-a177-f4f76e411514
Local pid:
ora:10771

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