{"id":{"repo_id":"greece","oai_identifier":"oai:10442/0699"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/0699","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥΣ","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Massouros, Christos","Μασούρος, Χρήστος"],"institution":"National Technical University of Athens (NTUA)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1988,"date_issued":"1988","date_published":"1988","updated_at":"2026-07-24T02:25:24Z","subjects":["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"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/0699"],"render_values":[{"text":"10.12681/eadd/0699","href":"https://doi.org/10.12681/eadd/0699","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/0699","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Massouros, Christos","Μασούρος, Χρήστος"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1988"]},{"key":"dc:publisher","label":"Institution","values":["National Technical University of Athens (NTUA)","Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["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"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/0699","http://hdl.handle.net/10442/hedi/0699"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","ΣΤΗ ΔΙΑΤΡΙΒΗ ΑΥΤΗ ΜΕΛΕΤΩΝΤΑΙ ΟΙ ΥΠΕΡΟΜΑΔΕΣ ΕΝ ΓΕΝΕΙ, ΚΑΘΩΣ ΚΑΙ ΟΡΙΣΜΕΝΕΣ ΕΙΔΙΚΕΣ ΚΑΤΗΓΟΡΙΕΣ ΥΠΕΡΟΟΜΑΔΩΝ (ΣΥΝΔΕΤΙΚΕΣ, ΟΜΟΙΟΓΕΝΕΙΣ, ΙΣΧΥΡΩΣ ΟΜΟΙΟΓΕΝΕΙΣ). ΑΠΟ ΤΗΘΕΩΡΙΑ ΠΟΥ ΑΝΑΠΤΥΣΣΕΤΑΙ ΠΡΟΚΥΠΤΟΥΝ ΣΥΜΠΕΡΑΣΜΑΤΑ ΣΤΟΥΣ ΓΡΑΜΜΙΚΟΥΣ ΧΩΡΟΥΣ, ΚΑΘΩΣΚΑΙ ΣΕ ΓΕΩΜΕΤΡΙΕΣ ΟΡΙΣΜΕΝΩΝ ΤΥΠΩΝ. ΣΗΜΑΝΤΙΚΟ ΡΟΛΟ ΣΤΗΝ ΟΛΗ ΜΕΛΕΤΗ ΠΑΙΖΟΥΝ ΟΙ ΗΜΙ-ΥΠΟ-ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΟΙ ΚΛΕΙΣΤΕΣ ΥΠΟ-ΥΠΕΡΟΜΑΔΕΣ, ΚΑΘΩΣ ΚΑΙ ΚΑΠΟΙΕΣ ΕΙΔΙΚΕΣ ΚΑΤΗΓΟΡΙΕΣ ΣΤΟΙΧΕΙΩΝ ΤΗΣ ΥΠΕΡΟΜΑΔΑΣ (ΟΠΩΣ ΤΑ ΘΕΜΕΛΙΩΔΗ, ΕΞΑΡΤΗΜΕΝΑ, ΣΥΣΧΕΤΙΣΜΕΝΑ Κ.Α.). ΓΙΑ ΤΑ ΣΤΟΙΧΕΙΑ ΑΥΤΑ ΔΙΑΤΥΠΩΝΟΝΤΑΙ ΘΕΩΡΗΜΑΤΑ ΠΟΥ ΠΕΡΙΓΡΑΦΟΥΝ ΤΗ ΣΥΜΠΕΡΙΦΟΡΑ ΤΟΥΣ (ΚΥΡΙΩΣ ΓΕΝΕΤΙΚΗ) ΜΕΣΑ ΣΤΗΝ ΥΠΕΡΟΜΑΔΑ. ΟΙ ΓΕΝΕΤΙΚΕΣ ΙΔΙΟΤΗΤΕΣ ΜΑΛΙΣΤΑ, ΜΕ ΤΙΣ ΟΠΟΙΕΣ ΕΙΝΑΙ ΕΦΟΔΙΑΣΜΕΝΑ ΤΑ ΣΤΟΙΧΕΙΑ ΚΑΠΟΙΩΝ ΕΙΔΙΚΩΝ ΥΠΕΡΟΜΑΔΩΝ ΟΔΗΓΗΣΑΝΣΤΗΝ ΕΙΣΑΓΩΓΗ ΚΑΙ ΤΗΝ ΜΕΛΕΤΗ ΤΩΝ ΟΜΟΙΟΓΕΝΩΝ ΚΑΙ ΤΩΝ ΙΣΧΥΡΩΣ ΟΜΟΙΟΓΕΝΩΝ ΥΠΕΡΟΜΑΔΩΝ. ΕΞΑΛΛΟΥ ΑΠΟΔΕΙΧΤΗΚΕ ΟΤΙ ΣΕ ΚΑΘΕ ΓΡΑΜΜΙΚΟ ΧΩΡΟ ΜΠΟΡΟΥΜΕ ΝΑ ΕΠΙΣΥΝΑΨΟΥΜΕ ΜΙΑΣΥΓΚΕΚΡΙΜΕΝΗ ΥΠΕΡΟΜΑΔΑ, ΤΗΝ ΠΡΟΣΔΕΔΕΜΕΝΗ ΥΠΕΡΟΜΑΔΑ ΤΟΥ ΓΡΑΜΜΙΚΟΥ ΧΩΡΟΥ. ΑΥΤΟ ΜΑΣ ΕΠΙΤΡΕΠΕΙ ΝΑ ΕΞΑΓΟΥΜΕ ΘΕΩΡΗΜΑΤΑ ΤΩΝ ΓΡΑΜΜΙΚΩΝ ΧΩΡΩΝ, ΟΠΩΣ ΤΩΝ KAKATANI, STONE, HELLY, RANDON, STEINITZ, ΚΑΡΑΘΕΟΔΩΡΗ ΩΣ ΠΟΡΙΣΜΑΤΑ ΠΟΛΥ ΓΕΝΙΚΟΤΕΡΩΝ ΘΕΩΡΗΜΑΤΩΝ, ΤΑ ΟΠΟΙΑ ΕΧΟΥΝ ΔΙΑΤΥΠΩΘΕΙ ΚΑΙ ΑΠΟΔΕΙΧΘΕΙ ΓΙΑ ΤΙΣ ΥΠΕΡΟΜΑΔΕΣ ΣΤΑ ΠΛΑΙΣΙΑ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΑΥΤΗΣ. ΣΤΟ ΤΕΛΕΥΤΑΙΟ ΚΕΦΑΛΑΙΟ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΓΙΝΕΤΑΙ ΜΙΑ ΣΥΝΟΨΗ ΟΛΩΝ ΤΩΝ ΓΝΩΣΤΩΝ ΜΕΘΟΔΩΝ ΚΑΤΑΣΚΕΥΗΣ ΥΠΕΡΣΩΜΑΤΩΝ ΚΑΙ ΕΠΙΠΛΕΟΝ ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΕΝΑ ΘΕΩΡΗΜΑ ΤΟ ΟΠΟΙΟ ΠΑΡΟΥΣΙΑΖΕΙ ΕΝΑ ΥΠΕΡΣΩΜΑ ΠΟΥ ΔΕΝ ΑΝΗΚΕΙ ΣΤΗΝ ΚΛΑΣΗ ΤΩΝ ΥΠΕΡΣΩΜΑΤΩΝ ΠΗΛΙΚΩΝ."]},{"key":"dc:title","label":"Title","values":["ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥΣ","HYPERGROUPS AND THEIR APPLICATIONS"]}]}],"canonical_facts":{"dc:creator":["Massouros, Christos","Μασούρος, Χρήστος"],"dc:date":["1988"],"dc:description":["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.","ΣΤΗ ΔΙΑΤΡΙΒΗ ΑΥΤΗ ΜΕΛΕΤΩΝΤΑΙ ΟΙ ΥΠΕΡΟΜΑΔΕΣ ΕΝ ΓΕΝΕΙ, ΚΑΘΩΣ ΚΑΙ ΟΡΙΣΜΕΝΕΣ ΕΙΔΙΚΕΣ ΚΑΤΗΓΟΡΙΕΣ ΥΠΕΡΟΟΜΑΔΩΝ (ΣΥΝΔΕΤΙΚΕΣ, ΟΜΟΙΟΓΕΝΕΙΣ, ΙΣΧΥΡΩΣ ΟΜΟΙΟΓΕΝΕΙΣ). ΑΠΟ ΤΗΘΕΩΡΙΑ ΠΟΥ ΑΝΑΠΤΥΣΣΕΤΑΙ ΠΡΟΚΥΠΤΟΥΝ ΣΥΜΠΕΡΑΣΜΑΤΑ ΣΤΟΥΣ ΓΡΑΜΜΙΚΟΥΣ ΧΩΡΟΥΣ, ΚΑΘΩΣΚΑΙ ΣΕ ΓΕΩΜΕΤΡΙΕΣ ΟΡΙΣΜΕΝΩΝ ΤΥΠΩΝ. ΣΗΜΑΝΤΙΚΟ ΡΟΛΟ ΣΤΗΝ ΟΛΗ ΜΕΛΕΤΗ ΠΑΙΖΟΥΝ ΟΙ ΗΜΙ-ΥΠΟ-ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΟΙ ΚΛΕΙΣΤΕΣ ΥΠΟ-ΥΠΕΡΟΜΑΔΕΣ, ΚΑΘΩΣ ΚΑΙ ΚΑΠΟΙΕΣ ΕΙΔΙΚΕΣ ΚΑΤΗΓΟΡΙΕΣ ΣΤΟΙΧΕΙΩΝ ΤΗΣ ΥΠΕΡΟΜΑΔΑΣ (ΟΠΩΣ ΤΑ ΘΕΜΕΛΙΩΔΗ, ΕΞΑΡΤΗΜΕΝΑ, ΣΥΣΧΕΤΙΣΜΕΝΑ Κ.Α.). ΓΙΑ ΤΑ ΣΤΟΙΧΕΙΑ ΑΥΤΑ ΔΙΑΤΥΠΩΝΟΝΤΑΙ ΘΕΩΡΗΜΑΤΑ ΠΟΥ ΠΕΡΙΓΡΑΦΟΥΝ ΤΗ ΣΥΜΠΕΡΙΦΟΡΑ ΤΟΥΣ (ΚΥΡΙΩΣ ΓΕΝΕΤΙΚΗ) ΜΕΣΑ ΣΤΗΝ ΥΠΕΡΟΜΑΔΑ. ΟΙ ΓΕΝΕΤΙΚΕΣ ΙΔΙΟΤΗΤΕΣ ΜΑΛΙΣΤΑ, ΜΕ ΤΙΣ ΟΠΟΙΕΣ ΕΙΝΑΙ ΕΦΟΔΙΑΣΜΕΝΑ ΤΑ ΣΤΟΙΧΕΙΑ ΚΑΠΟΙΩΝ ΕΙΔΙΚΩΝ ΥΠΕΡΟΜΑΔΩΝ ΟΔΗΓΗΣΑΝΣΤΗΝ ΕΙΣΑΓΩΓΗ ΚΑΙ ΤΗΝ ΜΕΛΕΤΗ ΤΩΝ ΟΜΟΙΟΓΕΝΩΝ ΚΑΙ ΤΩΝ ΙΣΧΥΡΩΣ ΟΜΟΙΟΓΕΝΩΝ ΥΠΕΡΟΜΑΔΩΝ. ΕΞΑΛΛΟΥ ΑΠΟΔΕΙΧΤΗΚΕ ΟΤΙ ΣΕ ΚΑΘΕ ΓΡΑΜΜΙΚΟ ΧΩΡΟ ΜΠΟΡΟΥΜΕ ΝΑ ΕΠΙΣΥΝΑΨΟΥΜΕ ΜΙΑΣΥΓΚΕΚΡΙΜΕΝΗ ΥΠΕΡΟΜΑΔΑ, ΤΗΝ ΠΡΟΣΔΕΔΕΜΕΝΗ ΥΠΕΡΟΜΑΔΑ ΤΟΥ ΓΡΑΜΜΙΚΟΥ ΧΩΡΟΥ. ΑΥΤΟ ΜΑΣ ΕΠΙΤΡΕΠΕΙ ΝΑ ΕΞΑΓΟΥΜΕ ΘΕΩΡΗΜΑΤΑ ΤΩΝ ΓΡΑΜΜΙΚΩΝ ΧΩΡΩΝ, ΟΠΩΣ ΤΩΝ KAKATANI, STONE, HELLY, RANDON, STEINITZ, ΚΑΡΑΘΕΟΔΩΡΗ ΩΣ ΠΟΡΙΣΜΑΤΑ ΠΟΛΥ ΓΕΝΙΚΟΤΕΡΩΝ ΘΕΩΡΗΜΑΤΩΝ, ΤΑ ΟΠΟΙΑ ΕΧΟΥΝ ΔΙΑΤΥΠΩΘΕΙ ΚΑΙ ΑΠΟΔΕΙΧΘΕΙ ΓΙΑ ΤΙΣ ΥΠΕΡΟΜΑΔΕΣ ΣΤΑ ΠΛΑΙΣΙΑ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΑΥΤΗΣ. ΣΤΟ ΤΕΛΕΥΤΑΙΟ ΚΕΦΑΛΑΙΟ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΓΙΝΕΤΑΙ ΜΙΑ ΣΥΝΟΨΗ ΟΛΩΝ ΤΩΝ ΓΝΩΣΤΩΝ ΜΕΘΟΔΩΝ ΚΑΤΑΣΚΕΥΗΣ ΥΠΕΡΣΩΜΑΤΩΝ ΚΑΙ ΕΠΙΠΛΕΟΝ ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΕΝΑ ΘΕΩΡΗΜΑ ΤΟ ΟΠΟΙΟ ΠΑΡΟΥΣΙΑΖΕΙ ΕΝΑ ΥΠΕΡΣΩΜΑ ΠΟΥ ΔΕΝ ΑΝΗΚΕΙ ΣΤΗΝ ΚΛΑΣΗ ΤΩΝ ΥΠΕΡΣΩΜΑΤΩΝ ΠΗΛΙΚΩΝ."],"dc:identifier":["10.12681/eadd/0699","http://hdl.handle.net/10442/hedi/0699"],"dc:language":["gre"],"dc:publisher":["National Technical University of Athens (NTUA)","Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ)"],"dc:subject":["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"],"dc:title":["ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥΣ","HYPERGROUPS AND THEIR APPLICATIONS"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:25:24Z"}