منابع مشابه
On splitting infinite-fold covers
Let X be a set, κ be a cardinal number and let H be a family of subsets of X which covers each x ∈ X at least κ times. What assumptions can ensure that H can be decomposed into κ many disjoint subcovers? We examine this problem under various assumptions on the set X and on the cover H: among other situations, we consider covers of topological spaces by closed sets, interval covers of linearly o...
متن کاملOn 2-fold covers of graphs
A regular covering projection ℘: X̃ → X of connected graphs is G-admissible if G lifts along ℘. Denote by G̃ the lifted group, and let CT(℘) be the group of covering transformations. The projection is called G-split whenever the extension CT(℘) → G̃ → G splits. In this paper, split 2-covers are considered, with a particular emphasis given to cubic symmetric graphs. Supposing that G is transitive o...
متن کاملOn the splittability of infinite covers
Let X be a set, κ be a cardinal number and let H a family of subsets of X which covers each x ∈ X at least κ times. Under what assumptions can we decompose H into κ many disjoint subcovers? We examine this problem under various assumptions on the set X and on the cover H: among other situations we consider covers of topological spaces by closed sets, interval covers of linearly ordered sets and...
متن کاملA Remark on Khovanov Homology and Two-fold Branched Covers
Examples of knots and links distinguished by the total rank of their Khovanov homology but sharing the same two-fold branched cover are given. As a result, Khovanov homology does not yield an invariant of two-fold branched covers. Mutation provides an easy method for producing distinct knots sharing a common two-fold branched cover: The mutation in the branch set corresponds to a trivial surger...
متن کامل(n,m)-Fold Covers of Spheres
A well known consequence of the Borsuk-Ulam theorem is that if the d-dimensional sphere S is covered with less than d + 2 open sets, then there is a set containing a pair of antipodal points. In this paper we provide lower and upper bounds on the minimum number of open sets, not containing a pair of antipodal points, needed to cover the d-dimensional sphere n times, with the additional property...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2011
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm212-2-1