General Topology and Its Relations to Modern Analysis and Algebra 2

Proceedings of the Second Prague Topological Symposium, 1966

Z. Frolík, V. Pták, M. Katětov

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9781483198507
• eBook ISBN:
  9781483223537
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

General Topology and Its Relations to Modern Analysis and Algebra II is comprised of papers presented at the Second Symposium on General Topology and its Relations to Modern Analysis and Algebra, held in Prague in September 1966. The book contains expositions and lectures that discuss various subject matters in the field of General Topology. The topics considered include the algebraic structure for a topology; the projection spectrum and its limit space; some special methods of homeomorphism theory in infinite-dimensional topology; types of ultrafilters on countable sets; the compactness operator in general topology; and the algebraic generalization of the topological theorems of Bolzano and Weierstrass. This publication will be found useful by all specialists in the field of Topology and mathematicians interested in General Topology.

Table of contents

• Front Cover
• General Topology and its Relations to Modern Analysis and Algebra II
• Copyright Page
• Table of Contents
• Foreword
• FROM THE REPORT OF THE ORGANIZING COMMITTEE
• LIST OF FOREIGN PARTICIPANTS
• LIST OF CZECHOSLOVAK PARTICIPANTS
• LIST OF COMMUNICATIONS
• CHAPTER 1. REMARKS ON AN ALGEBRAIC STRUCTURE FOR A TOPOLOGY
• CHAPTER 2. O PA3MEPHOCTH dm TOnOJIOrHHECKHX IIPOCTPAHCTB
• CHAPTER 3. PROJECTION-SPECTRA
• CHAPTER 4. SOME SPECIAL METHODS OF HOMEOMORPHISM THEORY IN INFINITE-DIMENSIONAL TOPOLOGY
• CHAPTER 5. POINT COUNTABLE OPEN COVERINGS IN COUNTABLY COMPACT SPACES
• CHAPTER 6. ON SOME RESULTS CONCERNING k-SPACES
• CHAPTER 7. REMARKS ON PRODUCT SPACES
• CHAPTER 8. PARACOMPACT SUBSETS
• CHAPTER 9. PROJECTIVE COVERS IN CERTAIN CATEGORIES OF TOPOLOGICAL SPACES
• CHAPTER 10. A HEREDITARILY INFINITE DIMENSIONAL SPACE
• CHAPTER 11. TWO CLASSES OF ALMOST PERIODIC FUNCTIONSON TOPOLOGICAL To-GROUPS
• CHAPTER 12. EINE FIXIERTE KURVE IN E3
• CHAPTER 13. CIRCUMSCRIBING CONVEX SETS
• CHAPTER 14. BEZIEHUNGEN ZWISCHEN GEWISSEN TOPOLOGIEN IN NOETHERSCHEN RINGEN
• CHAPTER 15. BOREL SUBSETS OF METRIC SEPARABLE SPACES
• CHAPTER 16. DIFFERENTIAL STRUCTURES
• CHAPTER 17. LOCALLY COMPACT REALCOMPACTIFICATIONS
• CHAPTER 18. SYNTOPOGENE HALBGRUPPEN
• CHAPTER 19. ABGESCHWÄCHTE TRENNUNGSAXIOME
• CHAPTER 20. RICHTUNGSRÄUME UND RICHTUNGSDIMENSION
• CHAPTER 21. ORDER STRUCTURES AND TOPOLOGICAL STRUCTURES
• CHAPTER 22. PRECLOSED MULTIVALUED MAPPINGS
• CHAPTER 23. ON URYSOHN'S LEMMA
• CHAPTER 24. ON FINITE To-SPACES
• CHAPTER 25. SOME NEW CONCEPTS OF DIMENSION AND THEIR GENERALIZATION
• CHAPTER 26. ON SEPARATION AND APPROXIMATION OF REAL FUNCTIONS DEFINED ON A CHOQUET SIMPLEX
• CHAPTER 27. EXTREMAL DISCONNECTEDNESS AND DYADICITY
• CHAPTER 28. QUELQUES DÉMONSTRATIONS NOUVELLES DANS LA THÉORIE DES ENSEMBLES BORELIENS
• CHAPTER 29. ÜBER DIE REALISIERUNG VON BOOLE-ALGEBREN ALS BOOLE-ALGEBREN REGULÄR OFFENER MENGEN
• CHAPTER 30. BAIRE SETS WHICH ARE BORELIAN SUBSPACES
• CHAPTER 31. TYPES OF ULTRAFILTERS ON COUNTABLE SETS
• CHAPTER 32. THE SPACE ßN AND THE CONTINUUM HYPOTHESIS
• CHAPTER 33. INTEGRATION IN TOPOLOGISCHEN VEKTORRÄUMEN UND LOKAL p-KONVEXEN ALGEBREN
• CHAPTER 34. ÜBER DIE QUOTIENTENTOPOLOGIE ALS SPUR DER POTENZ EINER TOPOLOGIE
• CHAPTER 35. THE COMPACTNESS OPERATOR IN GENERAL TOPOLOGY
• CHAPTER 36. O ΚΟΜΠΑΚΤΗΦΜΚΑΙίΜΗ IIPOCTPAHCTB BJIH30CTH
• CHAPTER 37. CONCERNING A CATEGORIAL APPROACH TO TOPOLOGICAL AND ALGEBRAIC THEORIES
• CHAPTER 38. UNIFORM DIMENSION OF MAPPINGS
• CHAPTER 39. GELFAND-NAIMARK THEOREMS FOR NON-COMMUTATIVE TOPOLOGICAL RINGS
• CHAPTER 40. CATEGORIAL METHODS IN TOPOLOGY
• CHAPTER 41. ΟΤΗΟΙΠΕΗΜΗ CME2KHOCTH H H-3ΑΜΚΗΥΤΜΕ PACÜ1HPEHHH
• CHAPTER 42. ALGEBRAS OF GERMS OF FOURIER TRANSFORMS
• CHAPTER 43. REMARKS ON A THEOREM OF B. POSPÍSIL
• CHAPTER 44. CONVERGENCE STRUCTURES
• CHAPTER 45. TOPOLOGICAL EMBEDDINGS IN EUCLIDEAN SPACE
• CHAPTER 46. CHARACTERIZATION OF FOURIER-STIELTJES TRANSFORMS OF VECTOR-VALUED MEASURES
• CHAPTER 47. ON CONVERGENCE TOPOLOGIES
• CHAPTER 48. ÜBER EIN KONVERGENZPRINZIP BEI SPEKTRALZERLEGUNGEN
• CHAPTER 49. ON DISCONTINUOUS SELECTORS
• CHAPTER 50. ON NUMERICAL AND NON-NUMERICAL ECART
• CHAPTER 51. HEKOTOPWE CBOMCTBA KOrOMOJIOrHHECKHX PA3MEPHOCTEH ΚΟΜΠΑΚΤΟΒ
• CHAPTER 52 ON QUASI-COMPONENTS
• CHAPTER 53. OB ΟΛΗΟΜ CBOñCTBE HYJIBMEPHMX METPHHECKHX nPOCTPAHCTB
• CHAPTER 54. ZUM EIGENWERTPROBLEM BEI ANALYTISCHEN OPERATORWERTIGEN FUNKTIONEN, DEREN KOEFFIZIENTEN POSITIVE OPERATOREN SIND
• CHAPTER 55. NOTE SUR LES ESPACES DE VOISINAGES (V) ET LES ORDRES SEMI-TOPOGÈNES
• CHAPTER 56. ON THE HAHN-MAZURKIEWICZ PROBLEM IN NON-METRIC SPACES
• CHAPTER 57. A FORMAL CONNECTION BETWEEN PROJECTIVENESS FOR COMPACT AND NOT NECESSARILY COMPACT COMPLETELY REGULAR SPACES
• CHAPTER 58. A SURVEY OF DIMENSION THEORY
• CHAPTER 59. ÜBER DIE POTENZEN Aα(0 ≤ α ≤ 1) EINES ABGESCHLOSSENEN OPERATORS AIN EINEM BANACHRAUM
• CHAPTER 60. IDEALTOPOLOGIEN AUF GEORDNETEN MENGEN
• CHAPTER 61. TOPOLOGICAL REPRESENTATION OF SEMIGROUPS
• CHAPTER 62. TWO THEOREMS OF THE DESCRIPTIVE THEORY OF POINT SETS
• CHAPTER 63. EIN KOMPAKTHEITSKRITERIUM FÜR ABBILDUNGSRÄUME MIT EINER VERALLGEMEINERTEN UNIFORMEN STRUKTUR
• CHAPTER 64. ΚΟΜΠΑΚΤΗΗΕ IIPE#CTABJIEHHfl ΗΕΠΡΕΡΜΒΗΜΧAJirEBPAHMECKHX CTPYKTYP
• CHAPTER 65. ON MEASURABLE SETS IN TOPOLOGICAL SPACES
• CHAPTER 66. ÜBER DIE VERALLGEMEINERTEN UNIFORMEN STRUKTUREN VON MORITA UND IHRE VERVOLLSTÄNDIGUNG
• CHAPTER 67. NORMALE ZAHLEN UND BAIRESCHE KATEGORIEN VON MENGEN
• CHAPTER 68. SYMMETRIC APPROACH TO THE FUNDAMENTAL NOTIONS OF GENERAL TOPOLOGY
• CHAPTER 69. UNIVERSAL SPACES
• CHAPTER 70. A NEW DIMENSION TYPE
• CHAPTER 71. TOPOLOGIES COMPATIBLE WITH ORDERING
• CHAPTER 72. SUR UNE GÉNÉRALISATION DE LA PROPRIÉTÉ DE DARBOUX
• CHAPTER 73. PROXIMITY AND CONSTRUCTION OF COMPACTIFICATIONS WITH GIVEN PROPERTIES1
• CHAPTER 74. THE SIMPLE DIMENSION OF A TOPOLOGICAL SPACE
• CHAPTER 75. PA3MEPHOCTL· H Μ5ΙΓΚΗΕ ΠΥΗΚΗ
• CHAPTER 76. NORMALITY AND PRODUCT SPACES
• CHAPTER 77. ÜBER EINE KLASSE LOKALKONVEXER RÄUME
• CHAPTER 78. STRUCTURE OF TCHEBYCHEV SETS1)
• CHAPTER 79. O KOHEHHOKPATHLIX OTOBPA^KEHMHX
• CHAPTER 80. ALGEBRAIC GENERALIZATION OF THE TOPOLOGICAL THEOREMS OF BOLZANO AND WEIERSTRASS