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Study of topological spaces with algebraic structures

Author: Dumbrăveanu Radu
Degree:doctor of physics and mathematics
Speciality: 01.01.04 - Geometry and topology
Scientific adviser: Mitrofan Cioban
doctor habilitat, professor
Institution: Tiraspol State University


The thesis was presented on the 25 August, 2015
Approved by NCAA on the 7 October, 2015


Adobe PDF document0.35 Mb / in romanian


CZU 515.122.4+515.126

Adobe PDF document 0.65 Mb / in romanian
114 pages


function spaces, topology of pointwise convergence, support, linear homeomorphisms, perfect properties, open-finite properties


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:

Scientific novelty and originality:
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: