Concepts inBounds on threshold dimension and disjoint threshold coverings (abstract only)

Hausdorff dimension

In mathematics, the Hausdorff dimension (also known as the Hausdorff¿Besicovitch dimension) is an extended non-negative real number associated with any metric space. The Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This means, for example, the Hausdorff dimension of a point is zero, the Hausdorff dimension of a line is one, and the Hausdorff dimension of the plane is two.
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Disjoint sets

In mathematics, two sets are said to be disjoint if they have no element in common. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets.
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Abstract art

Abstract art uses a visual language of form, color and line to create a composition which may exist with a degree of independence from visual references in the world. Western art had been, from the Renaissance up to the middle of the 19th century, underpinned by the logic of perspective and an attempt to reproduce an illusion of visible reality. The arts of cultures other than the European had become accessible and showed alternative ways of describing visual experience to the artist.
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Euclidean space

In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions. The term ¿Euclidean¿ distinguishes these spaces from the curved spaces of non-Euclidean geometry and Einstein's general theory of relativity, and is named for the Greek mathematician Euclid of Alexandria.
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Linear inequality

In mathematics a linear inequality is an inequality which involves a linear function.
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Time complexity

In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using big O notation, which suppresses multiplicative constants and lower order terms. When expressed this way, the time complexity is said to be described asymptotically, i.e. , as the input size goes to infinity.
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Vertex (graph theory)

In graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).
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