On local connectedness in hyperspaces

• Autorzy: Makuchowski W.
• Języki publikacji: EN

Abstrakty

EN

It is shown that for any Hausdorff compactum X in the hyperspace C(X) of subcontinua of X (in the hyperspace 2^X of all nonempty closed subsets of X) local connectedness and local arcwise connectedness are equivalent at any point. If X has the property of Kelley, then local connectedness of C(X) is proved to be equivalent to some stronger kinds of local connectedness and of local arcwise connectedness.

Słowa kluczowe

EN

compact; hyperspace of closed subsets; hyperspace of subcontinua; local arcwise connectedness; local connectedness; property of Kelley

PL

hiperprzestrzeń nieciągłości; hiperprzestrzeń podzbiorów domkniętych; miejscowe połączenie łukowe; topologia

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 2
• Strony: 119--126
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Makuchowski W.

• Opole University, Institute of Mathematics, Oleska 48, 45-052 Opole, Poland

Bibliografia

• [1] C. Dorsett, Local connectedness, connectedness im kleinen, and other properties of hyperspaces of R0 spaces, Mat. Vesnik, 31 (1979) 113-123.
• [2] C. Dorsett, Connectedness im kleinen, in hyperspaces, Math. Chronicle, 11 (1982) 31-36.
• [3] C. Dorsett, Local connectedness in hyperspaces, Rendiconti del Circolo Mate-matico di Palermo, 31 (1982) 137-144.
• [4] C. Dorsett, Connectivity properties in hyperspaces and product spaces, Fund. Math., 121 (1984) 189-197.
• [5] J. T. Goodykoontz Jr., Connectedness im kleinen and local connectedness in 2 and C(X), Pacific J. Math., 53 (1974) 387-397.
• [6] J. T. Goodykoontz Jr., More on connectedness im kleinen and local connectedness in C (X), Proc. Amer. Math. Soc., 65 (1977) 357-364.
• [7] J. T. Goodykoontz Jr., Local arcwise connectedness in 2x and C(X), Houston J. Math., 4 (1978) 41-47.
• [8] J. G. Hocking, G. S. Young, Topology, Addison-Wesley Publ. Co., 1961.
• [9] J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math., Soc., 52 (1942) 22-36.
• [10] K. Kuratowski, Topology, vol 2, Academic Press and PWN, Warszawa 1968.
• [11] A. K. Misra, C-supersets, piecewise order-arcs and local arcwise connectedness in hyperspaces, Q & A in General Topology, 8 (1990) 467-485.
• [12] S. B. Nadler Jr., Hyperspaces of sets, Marcel Dekker Inc., New York 1978.