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On properties of metrizable spaces X preserved by t ‐equivalence
Author(s) -
Marciszewski Witold
Publication year - 2000
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015886
Subject(s) - metrization theorem , mathematics , pointwise convergence , equivalence relation , pointwise , pure mathematics , polish space , borel equivalence relation , countable set , tychonoff space , discrete mathematics , equivalence (formal languages) , combinatorics , topological space , mathematical analysis , probability measure , separable space , borel measure , computer science , operating system , approx
For a completely regular space X , denote by C p ( X ) the space of continuous real valued functions on X , endowed with the pointwise convergence topology. The spaces X and Y are t ‐equivalent if C p ( X ) and C p ( Y ) are homeomorphic. It is proved that, for metrizable spaces X , the countable dimensionality is preserved by t ‐equivalence. It is also shown that this relation preserves absolute Borel classes greater than 2 and all projective classes.