منابع مشابه
Retractions onto series-parallel posets
The poset retraction problem for a poset P is whether a given poset Q containing P as a subposet admits a retraction onto P, that is, whether there is a homomorphism from Q onto P which fixes every element of P. We study this problem for finite series-parallel posets P. We present equivalent combinatorial, algebraic, and topological charaterisations of posets for which the problem is tractable,...
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For a Banach space B and for a class A of its bounded closed retracts, endowed with the Hausdorff metric, we prove that retractions on elements A ∈ A can be chosen to depend continuously on A, whenever nonconvexity of each A ∈ A is less than 1 2 . The key geometric argument is that the set of all uniform retractions onto an α−paraconvex set (in the spirit of E. Michael) is α 1−α −paraconvex sub...
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Trees with positively-weighted edges induce a natural metric on any subset of vertices, however not every metric is representable in this way. A problem arising in areas of classification, particularly in evolutionary biology, is how to approximate an arbitrary distance function by such a tree metric, and thereby estimate the underlying tree that generated the data. Such transformations, from d...
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The main result of this paper is a generalization of a theorem of R. S. Phillips [6] on the nonexistence of projections of l°° onto c0. If S is a locally compact Hausdorff space then let C(S) denote the space of bounded continuous real (or complex) valued functions on 5; also, let Co(S) be those functions in C(S) which vanish at infinity. If N is the space of positive integers with the discrete...
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For a fixed graph H, let Ret(H) denote the problem of deciding whether a given input graph is retractable to H. We classify the complexity of Ret(H) when H is a graph (with loops allowed) where each connected component has at most one cycle, i.e., a pseudoforest. In particular, this result extends the known complexity classifications of Ret(H) for reflexive and irreflexive cycles to general cyc...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1969-0239583-6