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ℵ‐completeness as E‐compactness via the Uniform Dimension a
Author(s) -
CONCILIO A. DI
Publication year - 1992
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.1749-6632.1992.tb32246.x
Subject(s) - mathematics , subspace topology , compact space , completeness (order theory) , metric space , cartesian product , tychonoff space , cardinality (data modeling) , discrete space , inductive dimension , class (philosophy) , discrete mathematics , dimension (graph theory) , space (punctuation) , normal space , metric (unit) , pure mathematics , topological vector space , mathematical analysis , topological space , computer science , minkowski–bouligand dimension , fractal dimension , artificial intelligence , operations management , economics , fractal , data mining , operating system
Let ℵ be an infinite cardinal number and ℛ (ℵ, 1) a complete metric space of density ℵ and uniform dimension 1 uniformly universal in the class of all metric spaces of density ≤ℵ and uniform dimension ≤ 1. The ℵ‐uniformity of a Tychonoff space X , which is generated by all open normal coverings of X with cardinality ≤ℵ, is complete iff X can be embedded as a closed subspace in a Cartesian product of copies of ℛ (ℵ, 1).