• Title/Summary/Keyword: hemiconnectedness

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HEMICOMPACTNESS AND HEMICONNECTEDNESS OF HYPERSPACES

  • Baik, B.S.;Hur, K.;Lee, S.W.;Rhee, C.J.
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.171-179
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    • 2000
  • We prove the following: (1) For a Hausdorff space X, the hyperspace K(X) of compact subsets of X is hemicompact if and only if X is hemicompact. (2) For a regular space X, the hyperspace $C_K(X)$ of subcontinua of X is hemicompact (hemiconnected) if and only if X is hemicompact (hemiconnected). (3) For a locally compact Hausdorff space X, each open set in X is hemicompact if and only if each basic open set in the hyperspace K(X) is hemicompact. (4) For a connected, locally connected, locally compact Hausdorff space X, K(X) is hemiconnected if and only if X is hemiconnected.

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