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On extension of continuous functions defined on a circle

✍ Scribed by E. P. Andriyuk


Publisher
Springer
Year
2004
Tongue
English
Weight
135 KB
Volume
56
Category
Article
ISSN
0041-5995

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Let C R (X) denote, as usual, the Banach algebra of all real valued continuous functions on a compact Hausdorff space X endowed with the supremum norm. We present an elementary proof of the following extension result for C R (X): For a given g ∈ C R (X) with zero set Zg and for the n-tuple (f1, . .

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In this paper we prove some properties of p -additive functions as well as p -additive set -valued functions. We start with some definitions. Definition 2.1. A set C βŠ† X (where X is a vector space) is said to be a convex cone if and only if C + C βŠ† C and t C βŠ† C for all t ∈ (0, ∞). Definition 2.2.