Certain questions related to the equivalence of local connectedness and connectedness im kleinen
نویسندگان
چکیده
منابع مشابه
Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces
We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...
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L. Dubins conjectured in 1984 that the graph on vertices {1 , 2 , 3 , . . . } where an edge isdrawn between vertices i and j with probability p i j = λ/max (i , j) independently for each pair iand j is a.s. connected for λ = 1. S. Kalikow and B. Weiss proved that the graph is a.s.connected for any λ > 1. We prove Dubin’s conjecture and show that the graph is a.s. connectedfo...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1964
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-13-2-211-216