Related papers: Effective dimension in some general metric spaces
The notion of effective topological complexity, introduced by B{\l}aszczyk and Kaluba, deals with using group actions in the configuration space in order to reduce the complexity of the motion planning algorithm. In this article we focus on…
We give a sharp Hausdorff content estimate for the size of the accessible boundary of any domain in a metric measure space of controlled geometry, i.e., a complete metric space equipped with a doubling measure supporting a $p$-Poincar\'e…
Supergales, generalizations of supermartingales, have been used by Lutz (2002) to define the constructive dimensions of individual binary sequences. Here it is shown that gales, the corresponding generalizations of martingales, can be…
We revisit the definition of effective local compactness, and propose an approach that works for arbitrary countably-based spaces extending the previous work on computable metric spaces. We use this to show that effective local compactness…
We present forms of the classical Riesz-Kolmogorov theorem for compactness that are applicable in a wide variety of settings. In particular, our theorems apply to classify the precompact subsets of the Lebesgue space $L^2$, Paley-Wiener…
Magnitude is a numerical invariant of finite metric spaces, recently introduced by T. Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of topological spaces. It has been extended…
We examine the analogues for the respective categories of locales of two well-known results about regularity and effectiveness of some categories of spaces. We show that the category of compact regular locales is effective regular…
We assume that the noncommutativity starts to be visible continuously from a scale $\Lambda_{NC}$. According to this assumption, a two-loop effective action is derived for noncommutative $\phi^{4}$ and $\phi^{3}$ theories from a Wilsonian…
The effects of extra space-time dimensions on the Wilsonian effective K\"ahler potential and the perturbative one loop effective K\"ahler potential are determined within the framework of an Abelian gauge theory with N=2 supersymmetric field…
Tchakaloff's theorem from 1957 asserts the existence of exact quadrature rules with non-negative weights for any polynomial space of finite degree on $\mathbb{R}^d$ if the underlying measure is positive, compactly supported, and absolutely…
V. V. Fedorchuk has recently introduced dimension functions K-dim \leq K-Ind and L-dim \leq L-Ind, where K is a simplicial complex and L is a compact metric ANR. For each complex K with a non-contractible join |K| * |K| (we write |K| for…
After calculating the Dushnik-Miller dimension of Minkowski spaces to be countable infinity, we define a novel notion of dimension for ordered spaces recovering the correct manifold dimension and obtain a corresponding obstruction for the…
The notion of the magnitude of a compact metric space was considered in arXiv:0908.1582 with Tom Leinster, where the magnitude was calculated for line segments, circles and Cantor sets. In this paper more evidence is presented for a…
We review the motivation and fundamental properties of the Hausdorff dimension of metric spaces and illustrate this with a number of examples, some of which are expected and well-known. We also give examples where the Hausdorff dimension…
We derive four-dimensional effective theories for warped compactification of the ten-dimensional IIB supergravity and the eleven-dimensional Horava-Witten model. We show that these effective theories allow a much wider class of solutions…
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
Calder\'on-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new approach for general measure spaces which admit a Markov…
In recent works, a framework has been developed to describe (quantum) deformed, spherically symmetric and static black holes in four dimensions. The key idea of this so-called Effective Metric Description (EMD) is to parametrise…
We suggest necessary conditions of soficness of multidimensional shifts formulated in termsof resource-bounded Kolmogorov complexity. Using this technique we provide examples ofeffective and non-sofic shifts on $\mathbb{Z}^2$ with very low…
By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite dimensional Hilbert space. We compare our general expressions with numerical…