Intuitionistic General Topology [PhD Thesis]

✍ Scribed by A.S. Troelstra

• Year: 1966
• Tongue: English
• Leaves: 115
• Category: Library

✦ Synopsis

In classical mathematics, one can more or less distinguish set theory in its most general form from topology as a specialization of general set theory. (We are aware, however, of the absence of a sharp borderline.)
In intuitionism, it is much more difficult to make such a distinction; predicates which might be considered as to belong to set theory in its most general form from a classical point of view can be used to describe "typically topological" properties in intuitionism. The contents of this thesis roughly correspond in classical topology to the contents of the first two chapters of de VRIES 1958.

✦ Table of Contents

Cover ......Page 1
Voorwoord ......Page 5
List of notations and conventions ......Page 6
List of notions ......Page 8
Bibliography ......Page 12
Introductory survey ......Page 14
1. Intuitionistic notions ......Page 20
2. Topological spaces ......Page 22
3. Metric spaces ......Page 26
4. Located pointspecies ......Page 29
1. Definitions ......Page 34
2. Basic pointspecies and point representations ......Page 36
3. Located compact spaces ......Page 38
1. Definition of intersection spaces ......Page 45
2. Representation and separation postulates ......Page 57
3. CIN- and PIN-spaces ......Page 70
4. Topological products ......Page 75
5. Examples ......Page 79
1. DFTK-spaces ......Page 88
2. LDFTK-spaces ......Page 97
3. Covering theorems ......Page 101
4. Located pointspecies and completeness ......Page 105
5. Topological products ......Page 108
Samenvatting ......Page 112
Stellingen ......Page 113