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CNAA / Theses / 2007 / May /

Algebraic and functional methods in the theory of extensions of topological spaces


Author: Laurenţiu Calmuţchi
Degree:doctor habilitat of physics and mathematics
Speciality: 01.01.04 - Geometry and topology
Year:2007
Scientific consultant: Mitrofan Cioban
doctor habilitat, professor, Tiraspol State University
Institution: Institute of Mathematics and Computer Science, Academy of Sciences of Moldova
Scientific council: DH 01-01.01.04
Institute of Mathematics and Computer Science, Academy of Sciences of Moldova

Status

The thesis was presented on the 25 May, 2007
Approved by NCAA on the 14 June, 2007

Abstract

Adobe PDF document0.34 Mb / in romanian

Thesis

CZU 515.12(043.3)

Adobe PDF document 1.11 Mb / in romanian
203 pages


Keywords

extension, g-extension, compactness, compactification, proximity, spectral space, remainder, uniform space, functor, ideal, filter, ring, semiring, base, nearness

Summary

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:

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.