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Compact semilattices with open principal filters

Part of: Peculiar spaces Topological and differentiable algebraic systems Generalities Semigroups

Published online by Cambridge University Press:  09 April 2009

Oleg V. Gutik ,
M. Rajagopalan  and
K. Sundaresan
Oleg V. Gutik
Affiliation:
Department of Algebra, Institute for Applied Problems, in Mechanics and Mathematics, National Academy of Sciences of Ukraine, 3b, Naukova Str., Lviv 79053, Ukraine e-mail: ogutik@iapmm.lviv.ua
M. Rajagopalan
Affiliation:
Department of Mathematics, Tennessee State University, 3500 John Merritt Boulevard, Nashville, TN 37209, USA e-mail: mrajagopalan@tnstate.edu
K. Sundaresan
Affiliation:
Department of Mathematics, Cleveland State University, Cleveland, OH 44115, USA e-mail: kondagunta@math.csuohio.edu
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Abstract

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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.

Keywords

topological semilatticecompact semilatticescattered spaceFranklin-Rajagopalan spaceonepoint Alexandroff compactification of a discrete spacetopological inverse semigroup

MSC classification

Secondary: 22A26: Topological semilattices, lattices and applications 20M18: Inverse semigroups 22A15: Structure of topological semigroups 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets) 54G12: Scattered spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 3 , June 2002 , pp. 349 - 362
Copyright
Copyright © Australian Mathematical Society 2002

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