A topological semigroup S is a thread if S is a metric arc in which one endpoint is the identity of S and the other endpoint is the zero of S. Let [x0, x1] and [y0, y1] be subsets of threads in a semigroup S. Then define A(x0, x1) = x ε [x0, x1] | xy1 = x1y for some y ε [y0, y[in1}]). The main result of this paper states that if X and Y are threads in a topological semigroup S, then XY is an arc or a point, or contains a two-cell.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Borrego, J. T., H. Cohen and E. E. DeVun,Uniquely Representable Semiqroups II, Pacific J. Math. 39 (1971), 573–580.
Brown, D. R. and M. Friedberg,Linear Representations of Certain Compact Semigroups, Trans. Amer. Math. Soc. 160 (1971), 453–465.
Clark, C. E.,Locally Algebraically Independent Collections of Subsemigroups of a Semigroup, Duke Math. J. 35 (1968), 843–851.
DeVun, E.,Special Semigroups on the Two-Cell, Pacific J. Math. 34 (1970), 639–646.
Faucett, W. M.,Compact Semigroups Irreducibly Connected between Two Idempotents, Proc. Amer. Math. Soc. 6 (1955), 741–747.
Hofmann, K. and P. S. Mostert,Elements of Compact Semigroups, Columbus, 1966.
Mostert, P. S. and A. L. Shields,On the Structure of Semigroups on a Compact Manifold with Boundary, Ann. of Math. 65 (1957), 117–143.
Wallace, A. D.,The Structure of Topological Semigroups, Bull. Amer. Math. Soc. 61 (1955), 95–112.
Whyburn, G. T.,Analytic Topology, Amer. Math. Soc. Colloq. Publ. 28, Providence, 1942.
This paper is part of the author's doctoral dissertation written under the direction of Professor D. R. Brown at the University of Houston. This work was supported in part by an NSF Science Faculty Fellowship.