A NOTE ON CONTINUOUS-MAPPINGS AND THE PROPERTY OF KELLEY,J.L.

被引：4
作者：
KATO, H
机构：
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1991年 / 112卷 / 04期
关键词：
HYPERSPACES OF CONTINUA; WHITNEY MAP; PROPERTY [K; CONTINUOUS SELECTION; WEAKLY CHAINABLE; UNIFORMLY PATHWISE CONNECTED;
D O I：
10.2307/2048666
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, it is proved that if X is a continuum and omega is any Whitney map for C(X), then the following are equivalent: (1) X has property [K]. (2) There exists a (continuous) mapping F: X x I x [0, omega(X)] --> C(X) such that F({x} x I x {t}) = {A is-an-element-of omega-1 (t)\x is-an-element-of A} for each x is-an-element-of X and t is-an-element-of [0, omega(X)], where I = [0, 1]. (3) For each t is-an-element-of [0, omega(X)], there is an onto map f: X x I --> omega-1 (t) such that f({x} x I) = {A is-an-element-of omega-1 (t)\x is-an-element-of A} for each x is-an-element-of X. Some corollaries are obtained also.
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页码：1143 / 1148
页数：6
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