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Extensions of Discrete Spaces
Author(s) -
PORTER JACK R.
Publication year - 1993
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.1749-6632.1993.tb52531.x
Subject(s) - linear subspace , extension (predicate logic) , space (punctuation) , mathematics , cardinality (data modeling) , simple (philosophy) , remainder , discrete space , character (mathematics) , closed set , pure mathematics , discrete mathematics , computer science , mathematical analysis , arithmetic , geometry , philosophy , epistemology , data mining , programming language , operating system
. A simple method is developed that embeds an H ‐closed space as the remainder of an H ‐closed extension of a discrete space; one of the many generated extensions will have the same cardinality, weight, density, and character as the original space. Also, an example of an H ‐closed space (an extension of a discrete space) is constructed in which the number of H ‐closed subspaces is less than the number of H ‐sets.