The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Paul D. Humke - One of the best experts on this subject based on the ideXlab platform.
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CONTRASTING SYMMETRIC POROSITY AND POROSITY
Journal of Applied Analysis, 1998Co-Authors: Michael J Evans, Paul D. HumkeAbstract:It is known that the following two fundamental properties of porosity fail for symmetric porosity: 1) Every nowhere dense set A contains a residual subset of points x at which A has porosity 1. 2) If A is a porous set and 0 < p < 1, then A can be written as a Countable Union of sets, each of which has porosity at least p at each of its points. Here we explore the somewhat surprising extent to which these properties fail to carry over to the symmetric setting and investigate what symmetric analogs do hold.
Michael J Evans - One of the best experts on this subject based on the ideXlab platform.
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CONTRASTING SYMMETRIC POROSITY AND POROSITY
Journal of Applied Analysis, 1998Co-Authors: Michael J Evans, Paul D. HumkeAbstract:It is known that the following two fundamental properties of porosity fail for symmetric porosity: 1) Every nowhere dense set A contains a residual subset of points x at which A has porosity 1. 2) If A is a porous set and 0 < p < 1, then A can be written as a Countable Union of sets, each of which has porosity at least p at each of its points. Here we explore the somewhat surprising extent to which these properties fail to carry over to the symmetric setting and investigate what symmetric analogs do hold.
N A Shirokov - One of the best experts on this subject based on the ideXlab platform.
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Approximation by Entire Functions on a Countable Union of Real-Axis Segments. 4. Inverse Theorem
Vestnik St. Petersburg University Mathematics, 2018Co-Authors: O V Silvanovich, N A ShirokovAbstract:For more than a century, the constructive description of functional classes in terms of the possible rate of approximation of its functions by means of functions chosen from a certain set remains among the most important problems of approximation theory. It turns out that the nonuniformity of the approximation rate due between the points of the domain of the approximated function is substantial. For instance, it was only in the mid-1950s that it was possible to constructively describe Holder classes on the segment [–1; 1] in terms of the approximation by algebraic polynomials. For that particular case, the constructive description requires the approximation at neighborhoods of the segment endpoints to be essentially better than the one in a neighborhood of its midpoint. A possible approximation quality test is to find out whether the approximation rate provides a possibility to reconstruct the smoothness of the approximated function. Earlier, we investigated the approximation of classes of smooth functions on a Countable Union of segments on the real axis. In the present paper, we prove that the rate of the approximation by the entire exponential-type functions provides the possibility to reconstruct the smoothness of the approximated function, i.e., a constructive description of classes of smooth functions is possible in terms of the specified approximation method. In an earlier paper, that result is announced for Holder classes, but the construction of a certain function needed for the proof is omitted. In the present paper, we use another proof; it does not apply the specified function.
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approximation by entire functions on Countable Unions of segments of the real axis 2 proof of the main theorem
Vestnik St. Petersburg University: Mathematics, 2017Co-Authors: O V Silvanovich, N A ShirokovAbstract:In this study, we consider an approximation of entire functions of Holder classes on a Countable Union of segments by entire functions of exponential type. It is essential that the approximation rate in the neighborhood of segment ends turns out to be higher in the scale that had first appeared in the theory of polynomial approximation by functions of Holder classes on a segment and made it possible to harmonize the so-called “direct” and “inverse” theorems for that case, i.e., restore the Holder smoothness by the rate of polynomial approximation in this scale. Approximations by entire functions on a Countable Union of segments have not been considered earlier. The first section of this paper presents several lemmas and formulates the main theorem. In this study, we prove this theorem on the basis of earlier given lemmas.
Warren B. Moors - One of the best experts on this subject based on the ideXlab platform.
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Fragmentability by the discrete metric
Bulletin of The Australian Mathematical Society, 2015Co-Authors: Warren B. MoorsAbstract:In a recent paper, topological spaces (X; ) that are fragmented by a metric that generates the discrete topology were investigated. In the present paper we shall continue this investigation. In particular, we will show, among other things, that such spaces are -scattered, that is, a Countable Union of scattered spaces, and characterise the continuous images of separable metrisable spaces by their fragmentability properties.
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Sigma-fragmentable spaces that are not Countable Unions of fragmentable subspaces
Topology and its Applications, 2002Co-Authors: Warren B. Moors, Scott ScifferAbstract:Abstract In this paper we show that although (l ∞ / c 0 ,weak) is sigma-fragmented by some metric it cannot be decomposed into countably many fragmentable subspaces. Likewise, we show that although the dual space of the continuous functions defined on the double arrow space is weak ∗ sigma-fragmented by some metric, it too cannot be decomposed into a Countable Union of fragmentable subspaces.
Dominique Lecomte - One of the best experts on this subject based on the ideXlab platform.
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A separation result for Countable Unions of Borel rectangles
The Journal of Symbolic Logic, 2019Co-Authors: Dominique LecomteAbstract:We provide dichotomy results characterizing when two disjoint analytic binary relations can be separated by a Countable Union of ${\bf\Sigma}^0_1 \!\times\! {\bf\Sigma}^0_\xi$ sets, or by a ${\bf\Pi}^0_1 \!\times\! {\bf\Pi}^0_\xi$ set.
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A separation result for Countable Unions of Borel rectangles
2017Co-Authors: Dominique LecomteAbstract:We provide dichotomy results characterizing when two disjoint analytic binary relations can be separated by a Countable Union of Σ 0 1 ×Σ 0 ξ sets, or by a Π 0 1 ×Π 0 ξ set.
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Descriptive complexity of Countable Unions of Borel rectangles
Topology and its Applications, 2014Co-Authors: Dominique Lecomte, Miroslav ZelenýAbstract:Abstract We give, for each Countable ordinal ξ ⩾ 1 , an example of a Δ 2 0 Countable Union of Borel rectangles that cannot be decomposed into countably many Π ξ 0 rectangles. In fact, we provide a graph of a partial injection with disjoint domain and range, which is a difference of two closed sets, and which has no Δ ξ 0 -measurable Countable coloring.
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Descriptive complexity of Countable Unions of Borel rectangles
arXiv: Logic, 2013Co-Authors: Dominique Lecomte, Miroslav ZelenýAbstract:We give, for each Countable ordinal $\xi \geq 1$, an example of a ${\bf\Delta}^0_2$ Countable Union of Borel rectangles that cannot be decomposed into countably many ${\bf\Pi}^0_\xi$ rectangles. In fact, we provide a graph of a partial injection with disjoint domain and range, which is a difference of two closed sets, and which has no ${\bf\Delta}^0_\xi$-measurable Countable coloring.
