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On locally compact shift-continuous topologies on the α-bicyclic monoid

On locally compact shift-continuous topologies on the α-bicyclic monoid AbstractA topology τ on a monoid S is called shift-continuous if for every a, b ∈ S the two-sided shift S → S, x ↦ axb, is continuous. For every ordinal α ≤ ω, we describe all shift-continuous locally compact Hausdorff topologies on the α-bicyclic monoid Bα. More precisely, we prove that the lattice of shift-continuous locally compact Hausdorff topologies on Bα is anti-isomorphic to the segment of [1, α] of ordinals, endowed with the natural well-order. Also we prove that for each ordinal α the α + 1-bicyclic monoid Bα+1 is isomorphic to the Bruck extension of the α-bicyclic monoid Bα. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Topological Algebra and its Applications de Gruyter

On locally compact shift-continuous topologies on the α-bicyclic monoid

Bardyla, Serhii
Topological Algebra and its Applications , Volume 6 (1): 9 – Apr 13, 2018
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Publisher
de Gruyter
Copyright
© 2018
ISSN
2299-3231
eISSN
2299-3231
DOI
10.1515/taa-2018-0003
Publisher site
See Article on Publisher Site

Abstract

AbstractA topology τ on a monoid S is called shift-continuous if for every a, b ∈ S the two-sided shift S → S, x ↦ axb, is continuous. For every ordinal α ≤ ω, we describe all shift-continuous locally compact Hausdorff topologies on the α-bicyclic monoid Bα. More precisely, we prove that the lattice of shift-continuous locally compact Hausdorff topologies on Bα is anti-isomorphic to the segment of [1, α] of ordinals, endowed with the natural well-order. Also we prove that for each ordinal α the α + 1-bicyclic monoid Bα+1 is isomorphic to the Bruck extension of the α-bicyclic monoid Bα.

Journal

Topological Algebra and its Applications – de Gruyter

Published: Apr 13, 2018

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