Search results for "General topology"
showing 10 items of 131 documents
A common extension of Arhangel'skii's Theorem and the Hajnal-Juhasz inequality
2019
AbstractWe present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s so…
A Riemann-Type Integral on a Measure Space
2005
In a compact Hausdorff measure space we define an integral by partitions of the unity and prove that it is nonabsolutely convergent.
On the Construction of Lusternik-Schnirelmann Critical Values with Application to Bifurcation Problems
1987
An iterative method to construct Lusternik-Schnirelmann critical values is presented. Examples of its use to obtain numerical solutions to nonlinear eigenvalue problems and their bifurcation branches are given. peerReviewed
Lyapunov graphs for circle valued functions
2018
International audience; Conley index theory is used to obtain results for flows associated to circular Lyapunov functions defined on general compact smooth n-manifolds. This is done in terms of their underlying circular Lyapunov digraphs, which are generalizations of Morse digraphs, by extensively studying their combinatorics, invariants and realizability.
Eberlein–Šmulian theorem and some of its applications
2014
Masteroppgave i matematikkdidaktikk – Universitetet i Agder 2014 The thesis is about Eberlein-Šmulian and some its applications. The goal is to investigate and explain different proofs of the Eberlein-Šmulian theorem. First we introduce the general theory of weak and weak* topology defined on a normed space X. Next we present the definition of a basis and a Schauder basis of a given Banach space. We give some examples and prove the main theorems which are needed to enjoy the proof of the Eberlein-Šmulian theorem given by Pelchynski in 1964. Also we present the proof given by Whitley in 1967. Next there is described the connection between the weak topology and the topology and the topology o…
Irregularity
2007
AbstractRegular and irregular pretopologies are studied. In particular, for every ordinal there exists a topology such that the series of its partial (pretopological) regularizations has length of that ordinal. Regularity and topologicity of special pretopologies on some trees can be characterized in terms of sets of intervals of natural numbers, which reduces studied problems to combinatorics.
Invariant Jordan curves of Sierpinski carpet rational maps
2015
In this paper, we prove that if $R\colon\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ is a postcritically finite rational map with Julia set homeomorphic to the Sierpi\'nski carpet, then there is an integer $n_0$, such that, for any $n\ge n_0$, there exists an $R^n$-invariant Jordan curve $\Gamma$ containing the postcritical set of $R$.
M-bornologies on L-valued Sets
2017
We develop an approach to the concept of bornology in the framework of many-valued mathematical structures. It is based on the introduced concept of an M-bornology on an L-valued set (X, E), or an LM-bornology for short; here L is an iccl-monoid, M is a completely distributive lattice and \(E: X\times X \rightarrow L\) is an L-valued equality on the set X. We develop the basics of the theory of LM-bornological spaces and initiate the study of the category of LM-bornological spaces and appropriately defined bounded “mappings” of such spaces.
Convergence of subdifferentials and normal cones in locally uniformly convex Banach space
2014
International audience; In this paper we study the behaviour of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch–Wets convergences. Our analysis is devoted to proximal, Fréchet, and Mordukhovich limiting normal cones and subdifferentials. The results obtained can be seen as extensions of the Attouch theorem to the context of non-convex functions on locally uniformly convex Banach space. They also generalize, to sequences of subsmooth sets or functions, various results in the literature.
Planar Sobolev homeomorphisms and Hausdorff dimension distortion
2011
We investigate how planar Sobolev-Orlicz homeomorphisms map sets of Hausdorff dimension less than two. With the correct gauge functions the generalized Hausdorff measures of the image sets are shown to be zero.