Vol. 24, No. 2, 1968

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ISSN: 0030-8730
A characterization of compact connected planar lattices

Charles E. Clark and Carl Eberhart

Vol. 24 (1968), No. 2, 233–240
Abstract

In this paper it is proved that every topological lattice on the two-cell is topologically isomorphic (iseomorphic) to a sublattice of the product lattice I × I. An explicit description of the compact connected sublattices of I × I containing (0,0) and (1, 1) is given. These results, together with a theorem of A. D. Wallace, yield a characterization of all compact connected lattices in the plane: each is iseomorphic to a sublattice of I × I.

Mathematical Subject Classification
Primary: 54.56
Secondary: 06.00
Milestones
Received: 2 May 1966
Published: 1 February 1968
Authors
Charles E. Clark
Carl Eberhart