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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.22 No.2

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A NOTE ON CONNECTEDNESS IM KLEINEN IN C(X)

A NOTE ON CONNECTEDNESS IM KLEINEN IN C(X)

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2015, v.22 no.2, pp.139-144
https://doi.org/10.7468/jksmeb.2015.22.2.139
BAIK, BONG SHIN (DEPARTMENT OF MATHEMATICS EDUCATION, WOOSUK UNIVERSITY)
RHEE, CHOON JAI (DEPARTMENT OF MATHEMATICS, WAYNE STATE UNIVERSITY)
BAIK, BONG SHIN, & RHEE, CHOON JAI. (2015). A NOTE ON CONNECTEDNESS IM KLEINEN IN C(X), 22(2), 139-144, https://doi.org/10.7468/jksmeb.2015.22.2.139

Abstract

Abstract. In this paper, we investigate the relationships between the space X and the hyperspace C(X) concerning admissibility and connectedness im kleinen. The following results are obtained: Let X be a Hausdorff continuum, and let A ∈ C(X). (1) If for each open set U containing A there is a continuum K and a neighborhood V of a point of A such that V ⊂ IntK ⊂ K ⊂ U, then C(X) is connected im kleinen. at A. (2) If IntA ≠ ø, then for each open set U containing A there is a continuum K and a neighborhood V of a point of A such that V ⊂ IntK ⊂ K ⊂ U. (3) If X is connected im kleinen. at A, then A is admissible. (4) If A is admissible, then for any open subset U of C(X) containing A, there is an open subset V of X such that A ⊂ V ⊂ ∪U. (5) If for any open subset U of C(X) containing A, there is a subcontinuum K of X such that A ∈ IntK ⊂ K ⊂ U and there is an open subset V of X such that A ⊂ V ⊂ ∪ IntK, then A is admissible.

keywords
hyperspace, connected im kleinen, admissible

참고문헌

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한국수학교육학회지시리즈B:순수및응용수학

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