Algebraic and functional methods in the theory of extensions of topological spaces
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StatusThe thesis was presented on the 25 May, 2007Approved by NCAA on the 14 June, 2007 Abstract – 0.34 Mb / in romanianThesisCZU 515.12(043.3)
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Keywords
extension, g-extension, compactness, compactification, proximity, spectral space, remainder, uniform space, functor, ideal, filter, ring, semiring, base, nearnessSummary
The thesis is devoted to general theory of extensions of arbitrary topological spaces, which is an important and still developing domain of topology. The general conception, examined in the work, allows to obtain the new results in the class of completely regular spaces, too. AII hypothesized topological spaces are assumed to be То-spaces in case we have no concrete indications. In the work are solved the following problems:
- are elaborated new methods of construction of extensions of distinct type: spectral extensions; pc-extensions; wa-compactifications;
- for any То-space are constructed and studied the Wallman compactification, the Choquet compactification, the Freudenthal-Morita compactification, the Stone-Cech g-compactification, the compactifications of Wallman-Shanin type, the compactification of Choquet type;
- are defined and examined distinct sorts of compactness: quasi-compactness, compact ness, strict compactness, double compactness, virtual minimal compactness, minimal compactness;
- are studied distinct topological functors and correspondences associated with exten sions;
- the special remainders of Hausdorff compactifications and uniform complete exten sions are studied;
- is introduced and studied the conception of wa-proximity for То-spaces.
In the thesis are utilized the method of filters, the method of ideals, funcţional methods, the methods of the lattice theory. Some problems formulated by P. S. Alexandroff, A. V. Arhangel'skii, M. M. Cioban and L. D. Nel are solved.
The main results of the work can be applied in the studying of extensions and mappings, in theory of funcţional spaces, in the theory of ideals and in a course on extensions of topological spaces.
A bibliography of about 219 items is included. The thesis is written in Romanian.
Oficial Reviewers
- Petru Soltan
doctor habilitat, professor, Moldova State University - Dumitru Botnaru
doctor habilitat, professor, Tiraspol State University - Miron R
academician, doctor docent în matematică, profesor universitar, Universitatea Al. I. Cuza, Iaşi, România
Theses
