Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 46 for “"Topological space"”.
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Some results on cardinality bounds and covering-type properties of a topological space.
… results on bounds for the cardinality of a topological space using cardinal functions. In particular, we give variations and improvements of the most known cardinality bounds for topological spaces. -In Section 1.1 we pose our attention on cardinality bounds for Urysohn spaces. In our work …
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Some selective and monotone versions of covering properties and some results on the cardinality of a topological space
… to the cardinality of particular classes of topological spaces.
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Metrization of ordered topological spaces
In 1969, Lutzer proved that a linearly ordered topological space with a Gδ-diagonal is metrizable. This appears to be the first work in the field of metrization of ordered topological spaces. Very little seems to have been done in this direction. This thesis is a study of the various conditions …
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Remainders and Connectedness of Ordered Compactifications
… Stone-Cech compactification oX of an ordered topological space X is constructed analogously to the Stone-Cech compactification X of a topological space X, and has similar properties. This technique requires a conceptual understanding of the Stone-Cech compactification and how its product …
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A new look at Counterexamples in topology
… in Topology is a useful catalogue of topological spaces and properties. This thesis extends that catalogue to the properties of sobriety and packedness, and describes some related theory. A purely topological account of sobriety and sober reflections is given, together with an account …
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A topological generalization of Schwarz' lemma
… families of transformations of a metrizable topological space into itself. But a geometrical interpretation of Zorn*s results is impossible without severe additional restrictions on the space and the families of transformations. The present paper proves a geometrical version of Schwarz' lemma …
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Covering properties and quasi-uniformities of topological spaces
… properties of compatible quasi-uniformities of a topological space. The covering properties considered in this work are orthocompactness, metacompactness and paracompactness; some generalizations of orthocompactness are also defined and studied.
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Topological Deep Learning: Graphs, Complexes, Sheaves
The types of spaces where data resides - graphs, meshes, grids, manifolds - are becoming increasingly varied and heterogeneous. Therefore, translating ideas, models, and theoretical results between different domains is becoming more and more challenging. Nonetheless, two fundamental principles …
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Equivariant LS-Category and Equivariant Topological Complexity
In this thesis we consider topological spaces endowed with an action of a topological group, and we develop a new concept to study these spaces. This concept is called orbit class and is often a good replacement for the well-known concept or- bit type. Using the concept of orbit class, we de ne a …
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Function spaces and a problem of banach
Function spaces have been a useful tool in probing the convergence of sequences of functions. The theory seems to have been triggered off by the works of Ascoli [36], Arzelà [37] and Hadamard [38]. In this thesis, we consider the space of continuous functions from a topological space X into the …
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Convergência em Espaços Topológicos: Redes e Filtros.
… to continuity concepts and the description of topological space itself, and these are some of the reasons for its outstanding revelance. We will discuss mainly about nets and lters. At long last, we will prove Tychono and Banach{Alaoglu{Bourbaki theorems that, besides result itself, reveal the …
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Fixed Points and Coincidences
… theorem for two maps from an arbitrary topological space to a manifold is given: the coincidence index is equal to the Lefschetz number. It follows that if the Lefschetz number of the pair is not zero then the maps have a coincidence. In Chapter 2 we introduce abstract convex structures …
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Realcompact Alexandroff spaces and regular σ-frames
… [1941) and [1943] introduced a concept of space, more general than topological space, in order to obtain a simple connection between a space and the system of real-valued functions defined on it. Such a connection aided the investigation of the relationships between the linear functionals …
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A quasi-pseudometrizability problem for ordered metric spaces
… obtain several results in the setting of ordered topological spaces related to the Hanai-Morita-Stone Theorem. The latter says that if f is a closed continuous map of a metric space X onto a topological space Y then the following statements are equivalent: (i) Y satisfies the first countability …
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A Structure Theorem for Bad 3-Orbifolds
… spherical boundary components and has underlying topological space S2 × I or (S2 × S1)\B3.</p>
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Ultrafilters and compactification
In this thesis, we construct the ultrafilter space of a topological space using ultrafilters as points, study some of its properties and describe a method of generating compactifications through the ultrafilter space. As part of investigating some properties of the ultrafilter space, we show that …
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Continuities on Subspaces
… declaring that for any family S of subsets of a topological space X, a function f : X → Y is S -continuous if for each S∈ S , the function f ↾ S : S → Y is continuous. This is easily seen to generalize such well known concepts as separate continuity and linear continuity. …
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Local properties of transitive quasi-uniform spaces
If (X,Ƭ) is a topological space, then a quasi-uniformity U on X is compatible with Ƭ if the quasi-uniform topology, Ƭ<sub>u</sub> = Ƭ. This paper is concerned with local properties of quasi-uniformities on a set X that are compatible with a given topology on X. Chapter II is devoted to the …
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