(L)-Semigroup Sums †
Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, 241 McLean Hall, Saskatoon, SK S7N 5E6, Canada
In this note, all spaces are Hausdorff, and the term map or mapping shall always mean continuous function.
Received: 12 November 2018 / Revised: 14 December 2018 / Accepted: 17 December 2018 / Published: 22 December 2018
An (L)-semigroup S
is a compact n
-manifold with connected boundary B
together with a monoid structure on S
such that B
is a subsemigroup of S
. The sum
of two (L)-semigroups S
having boundary B
is the quotient space obtained from the union of
by identifying the point
for each x
. It is shown that no (L)-semigroup sum of dimension less than or equal to five admits an H-space structure, nor does any (L)-semigroup sum obtained from (L)-semigroups having an Abelian boundary. In particular, such sums cannot be a retract of a topological group.
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Martin, J.R. (L)-Semigroup Sums . Axioms 2019, 8, 1.
Martin JR. (L)-Semigroup Sums . Axioms. 2019; 8(1):1.
Martin, John R. 2019. "(L)-Semigroup Sums ." Axioms 8, no. 1: 1.
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