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Cardinality and Structure of Semilattices of Ordered Compactifications
Author(s) -
MOONEY DOUGLAS D.,
RICHMOND THOMAS A.
Publication year - 1995
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1995.tb55906.x
Subject(s) - semilattice , cardinality (data modeling) , mathematics , tychonoff space , lattice (music) , maximal element , space (punctuation) , combinatorics , pure mathematics , discrete mathematics , topological space , set (abstract data type) , computer science , physics , semigroup , acoustics , data mining , programming language , operating system
Cardinalities and lattice structures which are attainable by semilattices of ordered compactifications of completely regular ordered spaces are examined. Visliseni and Flachsmeyer have shown that every infinite cardinal is attainable as the cardinality of a semilattice of compactifications of a Tychonoff space. Among the finite cardinals, however, only the Bell numbers are attainable as cardinalities of semilattices of compactifications. It is shown here that all cardinals, both finite and infinite, are attainable as the cardinalities of semilattices of ordered compactifications of completely regular ordered spaces. The last section examines lattice structures which are realizable as semilattices of ordered compactifications, such as chains and power sets.