منابع مشابه
The Suslinian Number and Other Cardinal Invariants of Continua
By the Suslinian number Sln(X) of a continuum X we understand the smallest cardinal number κ such that X contains no disjoint family C of non-degenerate subcontinua of size |C| ≥ κ. For a compact space X, Sln(X) is the smallest Suslinian number of a continuum which contains a homeomorphic copy of X. Our principal result asserts that each compact space X has weight ≤ Sln(X)+ and is the limit of ...
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We show that a planar unshielded compact set X is finitely Suslinian if and only if there exists a closed set F ⊂ S and a lamination ∼ of F such that F/∼ is homeomorphic to X. If X is a continuum, the analogous statement follows from Carathéodory theory and is widely used in polynomial dynamics.
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We show that each of the classes of hereditarily locally connected, finitely Suslinian, and Suslinian continua is Π1-complete, while the class of regular continua is Π4-complete.
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1. Surfaces containing a given volume. In an endeavour to simplify a proof of Liapounoff [2], to the effect that in the problem of the forms of equilibrium of rotating liquids the sphere would be the only form for a liquid at rest, Poincaré [ l ] was led to the consideration of electric capacities of solids of given volume, and arrived at the result that among such bodies the sphere would have ...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1984
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-124-2-123-129