ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥΣ

IN THIS DISSERTATION, THE HYPERGROUPS IN GENERAL, AS WELL AS SOME SPECIAL CATEGORIES OF HYPERGROUPS (JOIN, HOMIOGENE, STRONGLY HOMIOGENE) ARE STUDIED. BY THE DEVELOPED THEORY, CONCLUSIONS ARE DERIVED IN THE LINEAR SPACES, AS WELL AS IN CERTAIN GEOMETRIES. THE SEMI-SUB-HYPERGROUPS AND THE CLOSED SUB-HYPERGROUPS TOGETHER WITH SOME SPECIAL CATEGORIES OF ELEMENTS OF A HYPERGROUP (SUCH AS THE FUNDAMENTAL, DEPENDANT, CORRELATED ETC) PLAY A SIGNIFICANT ROLE IN THE WHOLE STUDY.THEOREMS ON THESE ELEMENTS, DESCRIBING THEIR PROPERTIES (MAINLY GENETIC) IN THE HYPERGROUP, ARE INTRODUCED. MOREOVER THE PROPERTIES WITH WHICH THE ELEMENTS OF SOME SPECIAL HYPERGROUPS ARE LED TO THE INTRODUCTION AND THE STUDY OF THE HOMIOGENE AND STRONGLY HOMIOGENE HYPERGROUPS. BESIDES IT WAS PROVED THAT IN EVERY LINEAR SPACE, CAN BE DEFINED. THIS ALLOWS US TO GET THEOREMS OF THE LINEAR SPACES SUCH AS THE THEOREMS OF KAKUTANI, STONE, HELLY, RANDON, CARATHEODORY, STEINITZ, WHICH DERIVE AS COROLLARIES OF MUCH MORE GENERAL THEOREMS OF THE HYPERGROUPS, THAT HAVE BEEN INTRODUCED AND PROVED, IN THE PROCESS OF THIS DISSERTATION. THE LAST CHAPTER OF THIS DISSERTATION IS A REVIEW OF ALL KNOWN METHODS OF CONSTRUCTING HYPERFIELDS. FURTHERMORE A THEOREM PRESENTING A HYPERFIELD NOT BELONGINGTO THE CLASS OF QUOTIENT HYPERFIELDS, IS PROVED.

Grantor dc:publisher

National Technical University of Athens (NTUA)

Year dc:date

1988

Authors dc:creator

• Massouros, Christos
• Μασούρος, Χρήστος

• ΓΡΑΜΜΙΚΟΙ ΥΠΟΧΩΡΟΙ
• ΓΡΑΜΜΙΚΟΙ ΧΩΡΟΙ
• ΗΜΙ-ΥΠΟ-ΥΠΕΡΟΜΑΔΑ
• ΚΛΕΙΣΤΗ ΥΠΟ-ΥΠΕΡΟΜΑΔΑ
• ΠΡΟΒΟΛΙΚΟΣ ΧΩΡΟΣ
• Σφαιρική γεωμετρία
• ΥΠΕΡΔΑΚΤΥΛΙΟΣ
• ΥΠΕΡΔΙΑΤΙΜΗΣΗ
• ΥΠΕΡΜΕΤΡΙΚΟΣ ΧΩΡΟΣ
• ΥΠΕΡΟΜΑΔΑ
• ΥΠΕΡΣΩΜΑ
• Convex sets
• HYPERFIELD
• HYPERGROUP
• HYPERMETRIC SPACE
• HYPERMODULES
• LINEAR SPACES
• LINEAR SUBSPACES
• PROJECTIVE SPACE#
• Spherical geometry
• Φυσικές Επιστήμες
• Μαθηματικά
• Natural Sciences
• Mathematics

Language dc:language

gre

Identifier

10.12681/eadd/0699

OAI identifier oai:identifier

oai:10442/0699