Nowhere dense sets and real-valued functions with closed graphs
نویسندگان
چکیده
منابع مشابه
On nowhere dense graphs
A set A of vertices of a graph G is called d-scattered in G if no two d-neighborhoods of (distinct) vertices of A intersect. In other words, A is d-scattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and recently it played a prominent role in the study of homomorphism preservation theorems for special cl...
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In this paper, we compare the computability and complexity of a continuous real function F with the computability and complexity of the graph G of the function F . A similar analysis will be carried out for functions on subspaces of the real line such as the Cantor space, the Baire space and the unit interval. In particular, we de1ne four basic types of e"ectively closed sets C depending on whe...
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Nowhere dense classes of graphs were introduced by Nešetřil and Ossona de Mendez as a model for “sparsity” in graphs. It turns out that nowhere dense classes of graphs can be characterised in many different ways and have been shown to be equivalent to other concepts studied in areas such as (finite) model theory. Therefore, the concept of nowhere density seems to capture a natural property of g...
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Many natural computational problems on graphs such as finding dominating or independent sets of a certain size are well known to be intractable, both in the classical sense as well as in the framework of parameterized complexity. Much work therefore has focussed on exhibiting restricted classes of graphs on which these problems become tractable. While in the case of undirected graphs, there is ...
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We consider the evaluation of first-order queries over classes of databases that are nowhere dense. The notion of nowhere dense classes was introduced by Nešetřil and Ossona de Mendez as a formalization of classes of “sparse” graphs and generalizes many well-known classes of graphs, such as classes of bounded degree, bounded treewidth, or bounded expansion. It has recently been shown by Grohe, ...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1989
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171289000013