Abstract
W. M. Faucett [1] 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 B-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.
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