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A
characterization of compact connected planar lattices
Charles E. Clark and Carl Eberhart |
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Vol. 24 (1968), No. 2, 233–240
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Abstract |
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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
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Milestones
Received: 2 May 1966
Published: 1 February 1968
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Authors |
| Charles E. Clark | |
| Carl Eberhart | |
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