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Algebraic Properties of the Uniform Closure of Spaces of Continuous Functions
Author(s) -
GARRIDO I.,
MONTALVO F.
Publication year - 1996
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.1749-6632.1996.tb36801.x
Subject(s) - subring , closure (psychology) , linear subspace , mathematics , algebraic number , context (archaeology) , property (philosophy) , pure mathematics , space (punctuation) , inverse , algebraic closure , algebra over a field , discrete mathematics , mathematical analysis , ring (chemistry) , computer science , geometry , paleontology , chemistry , differential algebraic equation , ordinary differential equation , organic chemistry , epistemology , economics , biology , differential equation , operating system , philosophy , market economy
For a completely regular space X , C ( X ) denotes the algebra of all real‐valued and continuous functions over X. This paper deals with the problem of knowing when the uniform closure of certain subsets of C ( X ) has certain algebraic properties. In this context we give an internal condition, “property A,” to characterize the linear subspaces whose uniform closure is an inverse‐closed subring of C ( X ).