Książka - szczegóły

CONTENTS
Introduction................................................................................................................................................. 3
I. TERMS AND NOTATION....................................................................................................................... 5
II. GROUPOIDS AND CATEGORIES...................................................................................................... 6
1. The notion of groupoid......................................................................................................................... 6
2. Equivalence of the definition of groupoid to the definition of Ehresmann.................................. 8
3. Relationship between l.lio notion of an liliroHiminn groupoid and the notion of a Brandt,
groupoid...................................................................................................................................................... 9
4. Categories of functions and representation theorems................................................................. 12
5. The algebraic product of sets and the closure of a sot in the multiplicative system............... 15
III. THE RELATIONSHIP BETWEEN A GOŁĄB PSEUDOOROUP AND AN EHRESMANN GROUPOID............................................................................................................... 16
6. The notions of a Gołąb pseudogroup and of a functional element............................................ 16
7. The isomorphism of an arbitrary Ehresmann groupoid and a Gołąb
pseudogroup of a certain type. Groupoids of functional elements................................................. 18
IV. GENERATING IN GOŁĄB PSEUDOGROUPS AND SOME PROPERTIES OF A SET OF FUNCTIONS.............................................................................................................................. 20
8. Some operations with sets of functions........................................................................................... 21
9. A quasi-order of the family of all subsets of the set, L (X)............................................................. 24
10. Determining a pseudogroups with the aid of sets of functional elements............................. 26
11. The problom of the existence of the smallest pseudogroup including a given set
of local homeomorphisms...................................................................................................................... 29
V. SEMI-PSEUDOGROUPS AND A GENERALIZATION OP THE NOTION OF AN ANALYTICAL STRUCTURE................................................................................................................ 33
12. Semi-pseudogroups......................................................................................................................... 33
13. The notion of an analytical structure............................................................................................... 35
References................................................................................................................................................. 39