186,804 research outputs found
Ultrametrics on Čech homology groups
No full textThis paper is devoted to introducing additional structure on Čech homology groups. First, we redefine the Čech homology groups in terms of what we have called approximative homology by using approximative sequences of cycles, just as Borsuk introduced shape groups using approximative maps. From this point on, we are able to construct complete ultrametrics on Čech homology groups. The uniform type (and then the group topology) generated by the ultrametric leads to a shape invariant which we use to deduce topological consequences.Ministerio de Economía, Comercio y Empresa (España)Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEinpres
Eduard Čech
No full textsummary:Jedná se o historický medajlonek věnovaný prof. Eduardu Čechovi. Především jeho práci a vlivu na výuku matematiky na českých školách a přípravu budoucích učitelů matematiky.summary:This is a historical medallion dedicated to prof. Eduard Čech. Especially to his work and influence on the teaching of mathematics in Czech schools and the training of future teachers of mathematics
The Stone-Čech compactification, the Stone-Čech remainder, and the regular Wallman property
No full textIn this paper, the following are proved: (1) the Stone-Čech compactification of a metrizable space is regular Wallman, (2) if the Stone-Čech compactification of a locally compact space whose pseudocompact closed subsets are compact is regular Wallman, then the Stone-Čech remainder is also regular Wallman. Consequently, the Stone-Čech remainder of a locally compact metrizable space is regular Wallman.</p
Stone-Čech compactifications via adjunctions
No full textThe Stone-Čech compactification of a space
X
X
is described by adjoining to
X
X
continuous images of the Stone-Čech growths of a complementary pair of subspaces of
X
X
. The compactification of an example of Potoczny from [P] is described in detail.</p
The effect of floods on the ichthyofauna of Štěpánovský stream
No full textThe effect of floods on the ichthyofauna of Štěpánovský stream (left-hand affluent of Sázava River, aver. summer flow rate 0.2 m3s-1) was studied using diet analysis of kingfisher A. atthis preying exclusively on local fish community. The first local flood event (2 August 2001; flow rate 100 m3s-1) caused drastic shift in the ichthyofauna composition from original fish community dominated by brown trout S. trutta, brook trout S. fontinalis and bullhead C. gobio to fish community dominated by bleak A. alburnus, roach R. rutilus, chub L. cephalus and gudgeon G. gobio. The second flood event (all Czech Republic floods in August 2002; flow rate 4 m3s-1) was surprisingly much less destructive to fish fauna. Consequently, the stream played also the role of refuge for many new fish species including juveniles of nase C. nasus, vimba bream V. vimba, barbel B. barbus, asp A. aspius and sunbleak L. delineatus, from highly flooded Sázava River
Maximum Betti numbers of Čech complexes
No full textThe Upper Bound Theorem for convex polytopes implies that the p-th Betti number of the Čech complex of any set of N points in ℝ^d and any radius satisfies β_p = O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions, which prove that this upper bound is asymptotically tight. For example, we describe a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of the Čech complex at the other radius is n²
The dilemma of the psychological and logical. On the didactic influence of Eduard Čech
No full textsummary:The article describes the author's considerations about two approaches to teaching mathematics which are inspired by several textbooks by Eduard Čech. Examples from the textbooks, methods of work with pupils and instructions for teachers are given. Čech's didactic work is briefly mentioned
P-punti nella compattificazione di Stone-Čech di ω
No full textNell'elaborato studiamo un approccio topologico a un problema di indipendenza di ZFC. Introduciamo quindi oltre agli strumenti preliminari, un'idea di come funzioni il forcing, una tecnica per mostrare consistenza e indipendenza di enunciati da una teoria, in particolare per quanto riguarda l'ipotesi del continuo, che ci servirà nel resto dell'elaborato. Approcciamo poi più concretamente lo studio degli ultrafiltri sull'insieme dei numeri naturali ω e le loro proprietà, per poi studiare caratteristiche e condizioni sufficienti all'esistenza di particolari ultrafiltri, detti p-punti. Osserviamo allora che l'insieme degli ultrafiltri, se dotato di una particolare topologia è un caso particolare di una compattificazione, detta compattificazione di Stone-Čech, che ha una proprietà universale di massimalità in termini di diagrammi commutativi, e che costruiamo in due differenti modi per coglierne meglio le proprietà e la struttura. Sotto quest'ottica andiamo infine a studiare le proprietà topologiche dei p-punti nella compattificazione di Stone-Čech di ω
Perfect images of Čech-analytic spaces
No full textA completely regular Hausdorff space X is Čech-analytic if X is the result of the Souslin operation applied to the locally compact sets in some (equivalently, any) compactification. We prove that Čech-analytic spaces are preserved under general perfect maps, thus settling a question raised by the late Z. Frolík.</p
Efficient construction of the Čech complex
No full textIn many applications, the first step into the topological analysis of a discrete point set P sampled from a manifold is the construction of a simplicial complex with vertices on P. In this paper, we present an algorithm for the efficient computation of the Čech complex of P for a given value ε of the radius of the covering balls. Experiments show that the proposed algorithm can generally handle input sets of several thousand points, while for the topologically most interesting small values of ε can handle inputs with tens of thousands of points. We also present an algorithm for the construction of all possible Čech complices on P
- …
