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

ISSN : 3059-0604

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Vol.20 No.1

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ON ARCWISE CONNECTEDNESS IM KLEINEN IN HYPERSPACES

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2013, v.20 no.1, pp.71-78
https://doi.org/10.7468/jksmeb.2013.20.1.71
Baik, Bong Shin
Rhee, Choon Jai
Baik,, B. S. , & Rhee,, C. J. (2013). ON ARCWISE CONNECTEDNESS IM KLEINEN IN HYPERSPACES, 20(1), 71-78, https://doi.org/10.7468/jksmeb.2013.20.1.71

Abstract

Let X be a space and $2^X$(C(X);K(X);$C_K$(X)) denote the hyperspace of nonempty closed subsets(connected closed subsets, compact subsets, subcontinua) of X with the Vietoris topology. We investigate the relationships between the space X and its hyperspaces concerning the properties of connectedness im kleinen. We obtained the following : Let X be a locally compact Hausdorff space. Let $x{\in}X$. Then the following statements are equivalent: (1) X is connected im kleinen at $x$. (2) $2^X$ is arcwise connected im kleinen at {$x$}. (3) K(X) is arcwise connected im kleinen at {$x$}. (4) $C_K$(X) is arcwise connected im kleinen at {$x$}. (5) C(X) is arcwise connected im kleinen at {$x$}.

keywords
hyperspace, connected im kleinen, arcwise connected im kleinen

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Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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