Ordinal Invariants in Topology.
- 1st ed.
- 1 online resource (172 pages)
- Memoirs of the American Mathematical Society ; v.32 .
- Memoirs of the American Mathematical Society .
Intro -- TABLE OF CONTENTS -- INTRODUCTION -- CHAPTER 1. ORDER OF A MAP -- 1.1. Definition and Elementary Results -- 1.2. Quotient Maps with Order ≤ 1 -- 1.3. Behavior of the Order of Quotient Maps -- 1.4. Examples and Exercises -- CHAPTER 2. E-ORDER -- 2.1. Definition and Elementary Properties -- 2.2. Spaces with E-order ≤ 1 -- 2.3. Behavior of E-order -- 2.4. The Least Upper Bound of E-orders -- CHAPTER 3. VIEW FROM CATEGORY THEORY -- 3.1. The Order of a Closure Space -- 3.2. The E-order in Terms of Categorical Notions -- 3.3. Order of a Map in Terms of Categorical Notions -- 3.4. One-to-One Correspondence Between E-orders and Certain Subcategories of CL -- 3.5. Canonical Attainment of E-order -- CHAPTER 4. MORE ABOUT E-ORDER -- 4.1. E-order at a Point -- 4.2. The E-order of a Brush -- 4.3. What Ordinals Appear as E-order -- 4.4. E-order and a Chain of Topologies -- 4.5. What Sets of Ordinals Appear -- CHAPTER 5. SPECIAL INSTANCES -- 5.1. Sequential Order -- 5.2. k-Order -- 5.3. m-Net Order -- 5.4. Some Instances of E-orders -- 5.5. Examples -- CHAPTER 6. SOME INVARIANTS FOR ALL SPACES -- 6.1. The Invariant σ -- 6.2. The Invariant ρ -- 6.3. The Invariant δ -- 6.4. The Invariant r -- MISCELLANEOUS EXERCISES -- LIST OF TABLES AND DIAGRAMS -- APPENDIX -- REFERENCES.