Compact semilattices with open principal filters

J. Austral. Math. Soc. 72 (2002), 349-362

Oleg V. Gutik
Department of Algebra
Institute for Applied Problems
in Mechanics and Mathematics
National Academy of Sciences of Ukraine
3b, Naukova Str., Lviv 79053
Ukraine
ogutik@iapmm.lviv.ua

M. Rajagopalan
Department of Mathematics
Tennessee State University
3500 John Merritt Boulevard
Nashville, TN 37209
USA
mrajagopalan@tnstate.edu

and

K. Sundaresan
Department of Mathematics
Cleveland State University
Cleveland, OH 44115
USA
kondagunta@math.csuohio.edu

Abstract

A locally compact semilattice with open principal filters is a zero-dimensional scattered space. Cardinal invariants of locally compact and compact semilattices with open principal filters are investigated. Structure of topological semilattices on the one-point Alexandroff compactification of an uncountable discrete space and linearly ordered compact semilattices with open principal filters are researched.

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