Abstract
In this note we shall show that if L is a locally compact connected distributive topological lattice of inductive dimension n and if the set of points at which L has dimension n has nonvoid interior, then the breadth of L is also n. Our terminology and notation used in this paper are the same as in [1] and [4]. It is well known that the number of elements in a finite Boolean algebra is always a power of two, and if there are 2n elements then there are exactly n atoms. It is also known that the center C of any lattice with 0 and 1 forms a Boolean lattice with the same 0 and 1, and that if L is a compact connected topological lattice of codimension n then the cardinal of C of L, hereafter denoted by Card(Cen(L)), is at most 2n, [4]. The following two lemmas have appeared in [4].
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