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Products of threads

Abstract

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.

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Additional information

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.

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Hinman, B. Products of threads. Semigroup Forum 8, 1–20 (1974). https://doi.org/10.1007/BF02194743

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Keywords

  • Topological Semigroup