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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2015.1
- 수록면
- 139 - 144 (6page)
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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 ≠∅ , 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.
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참고문헌 (13)
참고문헌 신청
C.J. Rhee / 1985 / Obstucting sets for hyperspace / Topology Proceedings 15 : 159 ~ 173
D.E. Bennett / 1977 / Continua and their non-separating subcontinua / Dissertationes Math. Rozprawy Mat 149 : 1 ~ 46
E. Michael / 1951 / Topologies on spaces of subsets / Trans. Amer. Math. Soc 71 : 152 ~ 182
G.T. Whyburn / 1942 / Analytic topology / Amer. Math. Soc. Colloq. Publication 28
J.T. Goodykoontz, Jr. / 1968 / Topology, Vol. II / Warszawa
D.E. Bennett / 1977 / Continua and their non-separating subcontinua / Dissertationes Math. Rozprawy Mat 149 : 1 ~ 46
E. Michael / 1951 / Topologies on spaces of subsets / Trans. Amer. Math. Soc 71 : 152 ~ 182
G.T. Whyburn / 1942 / Analytic topology / Amer. Math. Soc. Colloq. Publication 28
J.T. Goodykoontz, Jr. / 1968 / Topology, Vol. II / Warszawa
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