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A Note on Holsztyński's Theorem
Author(s) -
ARAUJO J.,
FONT J. J.,
HERNÁNDEZ S.
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.tb36792.x
Subject(s) - generalization , subspace topology , isometry (riemannian geometry) , mathematics , combinatorics , discrete mathematics , pure mathematics , mathematical analysis
In this note we provide an elementary proof of the following generalization of Holsztyński's theorem [2]: If there exists a linear isometry T of a completely regular subspace A of C 0 ( X ) into C 0 ( Y ), then there is a subset Y 0 of Y and a continuous map h of Y 0 onto X and a continuous map a: Y 0 → K , | a | = 1, such that ( Tf )( y ) = a ( y ) f ( h ( y )) for all y ∈ Y and all f ∈ A. As a consequence, we extend to C 0 ( X )‐spaces an old result by Myers [3].