Study of topological spaces with algebraic structures
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StatusThe thesis was presented on the 25 August, 2015Approved by NCAA on the 7 October, 2015 Abstract – 0.35 Mb / in romanianThesisCZU 515.122.4+515.126
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Keywords
function spaces, topology of pointwise convergence, support, linear homeomorphisms, perfect properties, open-finite propertiesSummary
This thesis is submitted to obtain a doctoral degree in Mathematics, specialty 111.04 - Geometry and Topology. It was elaborated at Tiraspol State University, in Chisinau, 2015.
Thesis structure: the thesis is written in Romanian and consists of an introduction, 3 chapters, conclusions, 87 bibliography titles, 104 pages of main text. The obtained results are published in 7 scientific papers.
Field of study of the thesis: belongs to the study of function spaces with algebraic structures properties and its applications.
Thesis aim and objectives:
- establishment of correlations between properties of spaces X, E and properties of function space Cp(X;E);
- determination of common properties of spaces X for which the function spaces Cp(X;E) are linear homeomorphic;
- determination of common properties of spaces X for which the topological rings Cp(X;E)are isomorphic.
Scientific novelty and originality:
- was developed a new method of research for function spaces with values in topological modules;
- were established some dual properties for certain classes of function spaces;
- were proved general theorems about topological properties which are preserved by linear equivalences.
The scientific problem solved consist of development a new methods for researching topological spaces with spaces with algebraic structures, which led to the establishment of correlations between properties of topological spaces and algebraic properties of function spaces with values in topological rings and modules.
The theoretical significance and applicative value of the thesis: consists in development of new research methods for spaces of functions with values in topological modules and establishment of general principles for preserving topological properties by linear equivalences.
The implementation of the scientific results:
- the results and methods developed in this thesis can be applied in further investigations of functional spaces;
- the results of the thesis can serve as support for master theses and can be used as content for some special courses for students from first and second cycle studies of mathematical specialties.
Oficial Reviewers
- Liubomir Chiriac
doctor habilitat, professor, Tiraspol State University - Florin Damian
doctor, associate professor (docent)
Council's Members
- Vladimir Arnautov, president
doctor habilitat, professor, Institute of Mathematics and Computer Science - Dorin Afanas, secretary
doctor, associate professor (docent) - Laurenţiu Calmuţchi, member
doctor habilitat, professor, Tiraspol State University - Dumitru Botnaru, member
doctor habilitat, professor, Tiraspol State University - Dorin Pavel , member
doctor, associate professor (docent)
Theses
