IJPAM: Volume 83, No. 2 (2013)
ON THE HILBERT CUBE
Prince of Songkla University
Pattani, 94000, THAILAND
Centre of Excellence in Mathematics
CHE, Si Ayutthaya Rd., Bangkok, 10400, THAILAND
Abstract. Given a positive odd integer with the Cantor ary set and the Cantor ary function are constructed. is a generalization of the Cantor set in the case that the measure of the set is still zero and defined on the Hilbert Cube is a generalization of the Cantor function. Also, for any let
and is the set of all singletons in Then is an upper semi continuous decomposition on the Hilbert Cube Moreover, is homeomorphic to
Received: September 1, 2012
AMS Subject Classification: 54C50
Key Words and Phrases: decomposition, upper semi continuous, Cantor ary set
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DOI: 10.12732/ijpam.v83i2.5 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395