Some semigroups on an 𝑛-cell

Abstract

The purpose of this paper is to prove a theorem which is a generalization of a theorem proved by the author in [5]. The latter theorem is a special case of the one presented here. The theorem to be proved is: Theorem. Let S be a semigroup which is topologically a closed n-cell, m ^2. Suppose for x and y in B, the bounding in-\)-sphere of S, xy = x. Then: (1) If S = K, the minimal ideal of S, then S consists entirely of left zeros, that is, xS = x for each x in S. (2) If S^K, then K is a deformation retract of S and K consists entirely of left zeros for S. Also there exists in S an I-semigroup T with the following properties : (i) S\K" = BT, where K° denotes the interior of K.