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Resolubilidade e irresolubilidade de espaços topológicos / Resolvable and irresolvable topological spacesBoero, Ana Carolina 09 March 2007 (has links)
O principal objetivo deste trabalho é apresentar um estudo sistemático da teoria dos espaços topológicos resolúveis e irresolúveis. Enfocaremos diversas propriedades inerentes aos mesmos, incluindo uma exposição meticulosa de técnicas utilizadas na construção de espaços topológicos irresolúveis e sem pontos isolados. Dado um cardinal \\kappa > 1, exibiremos exemplos de espaços topológicos que são \\kappa-resolúveis, mas que não são \\kappa^{+}-resolúveis. Mostraremos, ainda, que se um espaço topológico for n-resolúvel, para todo número natural n, o mesmo será \\omega-resolúvel. Provaremos, contudo, que se \\lambda é um cardinal tal que \\omega < cf(\\lambda) = \\lambda, existe um espaço topológico que é \\mu-resolúvel, para todo cardinal \\mu < \\lambda, mas que não é \\lambda-resolúvel. O cerne desta dissertação refere-se à construção, em ZFC, de um subespaço enumerável, denso e submaximal de 2^c. / The main purpose of this work is to study the theory of resolvable and irresolvable topological spaces. We shall introduce many properties of these spaces and we shall give special attention to some techniques used in the construction of irresolvable topological spaces without isolated points. Given a cardinal \\kappa > 1, we will present some examples of topological spaces which are \\kappa-resolvable, but not \\kappa^{+}-resolvable. Besides, we will show that if a topological space is n-resolvable, for every natural number n > 1, then it is \\omega-resolvable too. Nevertheless, we shall prove that if \\lambda is a cardinal with \\omega < cf(\\lambda) = \\lambda, there is a topological space which is \\mu-resolvable, for each cardinal \\mu < \\lambda, but that is not \\lambda-resolvable. The backbone of this dissertation is the construction, in ZFC, of a countable, dense and submaximal subspaces of 2^c.
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Resolubilidade e irresolubilidade de espaços topológicos / Resolvable and irresolvable topological spacesAna Carolina Boero 09 March 2007 (has links)
O principal objetivo deste trabalho é apresentar um estudo sistemático da teoria dos espaços topológicos resolúveis e irresolúveis. Enfocaremos diversas propriedades inerentes aos mesmos, incluindo uma exposição meticulosa de técnicas utilizadas na construção de espaços topológicos irresolúveis e sem pontos isolados. Dado um cardinal \\kappa > 1, exibiremos exemplos de espaços topológicos que são \\kappa-resolúveis, mas que não são \\kappa^{+}-resolúveis. Mostraremos, ainda, que se um espaço topológico for n-resolúvel, para todo número natural n, o mesmo será \\omega-resolúvel. Provaremos, contudo, que se \\lambda é um cardinal tal que \\omega < cf(\\lambda) = \\lambda, existe um espaço topológico que é \\mu-resolúvel, para todo cardinal \\mu < \\lambda, mas que não é \\lambda-resolúvel. O cerne desta dissertação refere-se à construção, em ZFC, de um subespaço enumerável, denso e submaximal de 2^c. / The main purpose of this work is to study the theory of resolvable and irresolvable topological spaces. We shall introduce many properties of these spaces and we shall give special attention to some techniques used in the construction of irresolvable topological spaces without isolated points. Given a cardinal \\kappa > 1, we will present some examples of topological spaces which are \\kappa-resolvable, but not \\kappa^{+}-resolvable. Besides, we will show that if a topological space is n-resolvable, for every natural number n > 1, then it is \\omega-resolvable too. Nevertheless, we shall prove that if \\lambda is a cardinal with \\omega < cf(\\lambda) = \\lambda, there is a topological space which is \\mu-resolvable, for each cardinal \\mu < \\lambda, but that is not \\lambda-resolvable. The backbone of this dissertation is the construction, in ZFC, of a countable, dense and submaximal subspaces of 2^c.
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Closure and compactness in framesMasuret, Jacques 03 1900 (has links)
Thesis (MSc (Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: As an introduction to point-free topology, we will explicitly show the connection
between topology and frames (locales) and introduce an abstract notion, which
in the point-free setting, can be thought of as a subspace of a topological space.
In this setting, we refer to this notion as a sublocale and we will show that there
are at least four ways to represent sublocales.
By using the language of category theory, we proceed by investigating closure
in the point-free setting by way of operators. We de ne what we mean by a coclosure
operator in an abstract context and give two seemingly di erent examples
of co-closure operators of Frm. These two examples are then proven to be the
same.
Compactness is one of the most important notions in classical topology and
therefore one will nd a great number of results obtained on the subject. We
will undertake a study into the interrelationship between three weaker compact
notions, i.e. feeble compactness, pseudocompactness and countable compactness.
This relationship has been established and is well understood in topology, but
(to a degree) the same cannot be said for the point-free setting. We will give the
frame interpretation of these weaker compact notions and establish a point-free
connection. A potentially promising result will also be mentioned. / AFRIKAANSE OPSOMMING: As 'n inleiding tot punt-vrye topologie, sal ons eksplisiet die uiteensetting van
hierdie benadering tot topologie weergee. Ons de nieer 'n abstrakte konsep wat,
in die punt-vrye konteks, ooreenstem met 'n subruimte van 'n topologiese ruimte.
Daar sal verder vier voorstellings van hierdie konsep gegee word.
Afsluiting, deur middel van operatore, word in die puntvrye konteks ondersoek
met behulp van kategorie teorie as taalmedium. Ons sal 'n spesi eke operator
in 'n abstrakte konteks de nieer en twee o enskynlik verskillende voorbeelde van
hierdie operator verskaf. Daar word dan bewys dat hierdie twee operatore dieselfde
is.
Kompaktheid is een van die mees belangrikste konsepte in klassieke topologie
en as gevolg daarvan geniet dit groot belangstelling onder wiskundiges. 'n Studie
in die verwantskap tussen drie swakker forme van kompaktheid word onderneem.
Hierdie verwantskap is al in topologie bevestig en goed begryp onder wiskundiges.
Dieselfde kan egter, tot 'n mate, nie van die puntvrye konteks ges^e word nie. Ons
sal die puntvrye formulering van hierdie swakker konsepte van kompaktheid en
hul verbintenis, weergee. 'n Resultaat wat moontlik belowend kan wees, sal ook
genoem word.
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Investigating Normality in Lattice Valued Topological SpacesHetzel, Luke 09 May 2022 (has links)
No description available.
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Lokalizace mobilního robota pomocí kamery / Mobile Robot Localization Using CameraVaverka, Filip January 2015 (has links)
This thesis describes design and implementation of an approach to the mobile robot localization. The proposed method is based purely on images taken by a monocular camera. The described solution handles localization as an association problem and, therefore, falls in the category of topological localization methods. The method is based on a generative probabilistic model of the environment appearance. The proposed solution is capable to eliminate some of the difficulties which are common in traditional localization approaches.
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Introduction to some modes of convergence : Theory and applicationsBolibrzuch, Milosz January 2017 (has links)
This thesis aims to provide a brief exposition of some chosen modes of convergence; namely uniform convergence, pointwise convergence and L1 convergence. Theoretical discussion is complemented by simple applications to scientific computing. The latter include solving differential equations with various methods and estimating the convergence, as well as modelling problematic situations to investigate odd behaviors of usually convergent methods.
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Borelovské množiny v topologických prostorech / Borel sets in topological spacesVondrouš, David January 2019 (has links)
This thesis deals with study of mappings preserving Borel classes or absolute Borel classes. We prove a theorem which shows that under some assumptions there exists a (selection) function with certain properties. Using this theorem we obtain several results on preservation of Borel classes. Moreover, thanks to that theorem we prove a theorem on preservation of absolute Borel classes under a perfect mapping. Next, we show an assertion which implies that a piecewise closed mapping has a restriction that is "piecewise perfect" and its image is equal to the image of the original mapping. Under certain additional assumptions we prove a similar assertion for an Fσ-mapping instead of a piecewise closed mapping. Using these assertions and the theorem on preservation of absolute Borel classes under a perfect mapping we obtain further results on preservation of absolute Borel classes, in particular, for piecewise closed mappings and Fσ- -mappings. In the last chapter we study mappings such that the inverse image of an open set under these mappings is of a particular additive class. 1
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On some results of analysis in metric spaces and fuzzy metric spacesAphane, Maggie 12 1900 (has links)
The notion of a fuzzy metric space due to George and Veeramani has many
advantages in analysis since many notions and results from classical metric space
theory can be extended and generalized to the setting of fuzzy metric spaces, for
instance: the notion of completeness, completion of spaces as well as extension of
maps. The layout of the dissertation is as follows:
Chapter 1 provide the necessary background in the context of metric spaces, while
chapter 2 presents some concepts and results from classical metric spaces in the
setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy
metric spaces, among others we show that: the product of two complete fuzzy metric
spaces is also a complete fuzzy metric space.
Our main contribution is in chapter 4. We introduce the concept of a standard
fuzzy pseudo metric space and present some results on fuzzy metric identification.
Furthermore, we discuss some properties of t-nonexpansive maps. / Mathematical Sciences / M. Sc. (Mathematics)
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A classification of localizing subcategories by relative homological algebraNadareishvili, George 16 October 2015 (has links)
No description available.
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On some results of analysis in metric spaces and fuzzy metric spacesAphane, Maggie 12 1900 (has links)
The notion of a fuzzy metric space due to George and Veeramani has many
advantages in analysis since many notions and results from classical metric space
theory can be extended and generalized to the setting of fuzzy metric spaces, for
instance: the notion of completeness, completion of spaces as well as extension of
maps. The layout of the dissertation is as follows:
Chapter 1 provide the necessary background in the context of metric spaces, while
chapter 2 presents some concepts and results from classical metric spaces in the
setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy
metric spaces, among others we show that: the product of two complete fuzzy metric
spaces is also a complete fuzzy metric space.
Our main contribution is in chapter 4. We introduce the concept of a standard
fuzzy pseudo metric space and present some results on fuzzy metric identification.
Furthermore, we discuss some properties of t-nonexpansive maps. / Mathematical Sciences / M. Sc. (Mathematics)
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