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 61 for “"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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Compact topological spaces inspired by combinatorial constructions
Due to Mr�owka [24], polyadic spaces are compact Hausdor� spaces that are continuous images of some power of the one point compactication� of a discrete space �. It turns out that many results about polyadic spaces hold for a more general class spaces, as we shall show in this thesis. For a …
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DW complexes and their underlying topological spaces
… stems from an analogue in the category of topological spaces: the so-called CW complex (introduced by J.H.C. Whitehead in 1949).
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Effective computation of invariants of finite topological spaces
En este trabajo hemos presentado algoritmos efectivos para el cálculo de invariantes de espacios topológicos finitos. Estos algoritmos han sido desarrollados por medio de la combinación de técnicas combinatorias sobre posets, las cuales han sido establecidas en los trabajos que fundamentan la …
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Examples and theorems for generalized paracompact topological spaces
… of unsolved problems in generalized paracompact topological spaces. Examples satisfying the T₄ separation axiom are constructed showing the relationship between the properties B(D, ω₀)-refinability, B(D, λ)-refinability, and weak θ̅-refinability. The properties B(D, λ)-refinability and weak …
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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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FINITELY ADDITIVE MEASURES ON TOPOLOGICAL SPACES AND BOOLEAN ALGEBRAS
… algebras and the induced measures on their Stone spaces is mentioned in this chapter. We also show that for any charge algebra, there exists a compact zero-dimensional space such that its charge algebra is isomorphic to the given charge algebra. In Chapter three, we give the de�nition of Jordan …
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The property B(P,[alpha])-refinability and its relationship to generalized paracompact topological spaces
The property B(P,∝)-refinability is studied and is used to obtain new covering characterizations of paracompactness, collectionwise normality, subparacompactness, d-paracompactness, a-normality, mesocompactness, and related concepts. These new characterizations both generalize and unify many …
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Coverings and Descent Theory of Finite Spaces
… of the reflection of the category of finite topological spaces into the category of discrete finite topological spaces. This turns out to be nothing but the equivalence between the category of coverings of a connected finite topological space and the actions of the fundamental group of that …
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(Strongly) zero-dimensional ordered spaces
The relationship between transitive uniform spaces and zero-dimensional topological spaces was first established by Banaschewski [1957], and was later investigated by Levine [1969]. The theory of transitive quasi-uniform spaces is treated in [Fletcher and Lindgren 1972], [Brummer 1984] and [Kiinzi …
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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 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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Interior algebras and topology
… of interior algebras and categories of topological spaces, and generalizations of topological concepts to interior algebras, are investigated. The following are some of the most significant results we obtain: The establishment of a duality between topological spaces and complete atomic …
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Strict extensions in pointfree topology
Extensions of spaces have been constructed and used since the 19th century, for example, to form the complex sphere from the complex plane by adding a point at in nity. Once topological spaces were invented in the 20th century, completions and compactications became important examples of …
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Problems in the Theory of Convergence Spaces
… several problems in the theory of convergence spaces: generalization of Kolmogorov separation from topological spaces to convergence spaces, representation of reflexive digraphs as convergence spaces, construction of differential calculi on convergence spaces, mereology on convergence spaces, …
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A Relation-Algebraic Approach to L - Fuzzy Topology
… of an L - fuzzy topology, consider bases of topological spaces, continuous maps, and the first two separation axioms T0 and T1. The resulting theory of L - fuzzy topological spaces provides the foundation for applications and algorithms in areas such as digital topology, i.e., analyzing …
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On the Homotopy Theory of Stratified Spaces
… to proving a 'homtopy hypothesis' for stratified spaces. Specifically, given a poset P, we show that the ∞-category Strₚ of ∞-categories with a conservative functor to P can be obtained from the ordinary category of P-stratified topological spaces by inverting a class of weak equivalences. For …
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On paracompactness
… The important problem of the metrization of topological spaces is presented as an application of the concept of paracompactness.
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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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