On analogues of some classical subsets of the real line

• Autorzy: Kharazishvili A. B.
• Języki publikacji: EN

Abstrakty

EN

A theorem on the existence of separable supports of σ-finite Borel measures given on metric spaces with small topological weights is applied to constructions of certain analogues of special subsets of the real line.

Słowa kluczowe

EN

separable support of a measure; Luzin set; Sierpiński set; universal measure zero space

PL

zbiór Luzina; zbiór Sierpińskiego; uniwersalna miara przestrzeni zero

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2000
• Tom: Vol. 6, nr 1
• Strony: 77--85
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kharazishvili A. B.

• Institute of Applied Mathematics of Tbilisi State University University Str. 2 380043 Tbilisi 43 Republic of Georgia

Bibliografia

• [1] Cox, G.V., A universal null graph whose domain has positive measure, Colloq. Math. 46(2) (1982), 181-184.
• [2] Halmos, P.R., Measure Theory, D. Van Nostrand, Princeton — New York, 1950.
• [3] Hewitt, E., Ross, K., Abstract Harmonic Analysis, Vol. 1, Springer-Verlag, Berlin, 1963.
• [4] Kharazishvili, A.B., Remark on Luzin sets and Sierpiński sets, Bull. Georgian Acad. Sci. 143(3) (1991), (in Russian).
• [5] Kharazishvili, A.B., Generalized Sierpiński sets, Proc. Georgian Acad. Sci. Math. 1(5) (1993).
• [6] Kunen, K., Set Theory, North-Holland, Amsterdam, 1980.
• [7] Kuratowski, K., Topology, Vol. 1, Academic Press, New York — London, 1966.
• [8] Miller, A.W., Special subsets of the real line, in: “Handbook of Set-Theoretic Topology”, North-Holland, Amsterdam, 1984.
• [9] Morgan II, J.C., Point Set Theory, Marcel Dekker, Inc., New York — Basel, 1990.
• [10] Oxtoby, J.C., Measure and Category, Springer-Verlag, Berlin, 1971.