Root closed function algebras on compacta of large dimension
Authors:
N. Brodskiy, J. Dydak, A. Karasev and K. Kawamura
Journal:
Proc. Amer. Math. Soc. 135 (2007), 587596
MSC (2000):
Primary 54F45; Secondary 46J10
Published electronically:
August 8, 2006
MathSciNet review:
2255306
Fulltext PDF Free Access
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Abstract: Let be a Hausdorff compact space and let be the algebra of all continuous complexvalued functions on , endowed with the supremum norm. We say that is (approximately) th root closed if any function from is (approximately) equal to the th power of another function. We characterize the approximate th root closedness of in terms of divisibility of the first Cech cohomology groups of closed subsets of . Next, for each positive integer we construct an dimensional metrizable compactum such that is approximately th root closed for any . Also, for each positive integer we construct an dimensional compact Hausdorff space such that is th root closed for any .
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Additional Information
N. Brodskiy
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
Email:
brodskiy@math.utk.edu
J. Dydak
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
Email:
dydak@math.utk.edu
A. Karasev
Affiliation:
Department of Mathematics, Nipissing University, North Bay, Ontario, Canada P1B 8L7
Email:
alexandk@nipissingu.ca
K. Kawamura
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 3058071, Japan
Email:
kawamura@math.tsukuba.as.jp
DOI:
http://dx.doi.org/10.1090/S0002993906084905
PII:
S 00029939(06)084905
Keywords:
Algebraically closed algebras,
approximately root closed algebras,
commutative Banach algebras,
dimension
Received by editor(s):
June 5, 2005
Received by editor(s) in revised form:
August 31, 2005
Published electronically:
August 8, 2006
Additional Notes:
The third author was partially supported by an NSERC Grant.
Communicated by:
Alexander N. Dranishnikov
Article copyright:
© Copyright 2006
American Mathematical Society
