Related papers: Brouwer and Cardinalities
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely, Maria L. Rizzo [arXiv:1010.0297]
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
While Peano's negative attitude towards infinitesimals, in particular, geometric infinitesimals, is widely documented, his conception of a single infinite cardinality and, more generally, his views on the infinite, are a lot less known. The…
Rauzy classes define a partition of the set of irreducible (or indecomposable) permutations. They were defined by G. Rauzy as part of an induction algorithm for interval exchange transformations. In this article we prove an explicit formula…
Four constructions result from a desire to create enhancements to Cantor's infinite real set cardinality. Each continues to keep Cantor's cardinality formulation in place while providing new comparisons of arbitrary infinite sets. To…
A set $Q$ in $\mathbb{Z}_+^d$ is a lower set if $(k_1,\dots,k_d)\in Q$ implies $(l_1,\dots,l_d)\in Q$ whenever $0\le l_i\le k_i$ for all $i$. We derive new and refine known results regarding the cardinality of the lower sets of size $n$ in…
We show that various tameness assertions about abstract elementary classes imply the existence of large cardinals under mild cardinal arithmetic assumptions.
Under large cardinal hypotheses beyond the Kunen inconsistency -- hypotheses so strong as to contradict the Axiom of Choice -- we solve several variants of the generalized continuum problem and identify structural features of the levels…
We extend to the infinite dimensional context the link between two completely different topics recently highlighted by the authors: the classical eigenvalue problem for real square matrices and the Brouwer degree for maps between oriented…
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]
For a right invariant distance on a permutation space $S_n$ we give a sufficient condition for the cardinality of a ball of radius $R$ to grow polynomially in $n$ for fixed $R$. For the distance $\ell_1$ we show that for an integer $k$ the…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for…
In this article, we give an introduction to the notion of ambidexterity and norm map, and construct inductively the canonical norm map for $m$-truncated maps for some $m\geq-1$, on which the definitions of integration and cardinality are…
Discussion on "Brownian distance covariance" by G\'abor J. Sz\'ekely and Maria L. Rizzo [arXiv:1010.0297]
This paper replies the comment by E. Kapuscik [Am. J. Phys. 77, 754 (2009)]