On the kernel of a topological semigroup with cut points
Yatarō Matsushima · Proceedings of the American Mathematical Society · 1961
l] recently studied the structure of the kernel of a compact connected mob which has a point that cuts the kernel.L. W. Anderson [2] has characterized the cut point of a connected topological lattice.The main purpose of this paper is to find a lattice theoretic characterization of the kernel by means of cut points in the topological semigroups derived from topological lattices.Using the concept of E-covers [3], we shall define a suitable multiplication in topological lattices to illustrate the structure of the kernel by lattice diagrams.The fact that a special case of Faucett's Theorem (Theorem 2) can be obtained from Anderson's result (Lemma 5) is important.