Vol. 44, No. 1, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Decomposition of semilattices with applications to topological lattices

Joe Bill Rhodes

Vol. 44 (1973), No. 1, 299–307

Every element with finite extent in a meet-continuous semilattice with complete chains is the meet of a finite number of meet irreducibles. This includes both semilattices with the ascending chain condition and compact topological semilattices with finite breadth. By applying this decomposition to topological lattices on an n-cell, the following results are obtained: If L and M are topological lattices on n and m-cells respectively and there is an order isomorphism between the boundaries of L and M, then L and M are homeomorphic. If, in addition, L and M are distributive, L and M are isomorphic.

Mathematical Subject Classification
Primary: 06A20
Received: 6 May 1971
Published: 1 January 1973
Joe Bill Rhodes