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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Polynomials and limited sets

Author: Pablo Galindo
Journal: Proc. Amer. Math. Soc. 124 (1996), 1481-1488
MSC (1991): Primary 46G20; Secondary 46B20
MathSciNet review: 1307518
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Abstract: We prove that scalar-valued polynomials are weakly continuous on limited sets and that, as in the case of linear mappings, every $c_0$-valued polynomial maps limited sets into relatively compact ones. We also show that a scalar-valued polynomial whose derivative is limited is weakly sequentially continuous.

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Pablo Galindo

Keywords: Polynomial, limited set, weakly conditionally compact set
Received by editor(s): June 13, 1994
Received by editor(s) in revised form: October 19, 1994
Additional Notes: The author was supported in part by DGICYT pr. 91-0326 and by grant 93-081
Communicated by: Theodore Gamelin
Article copyright: © Copyright 1996 American Mathematical Society