Categories, groupoids, pseudogroups and analytical structures

W. Waliszewski

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1965

Abstract

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CONTENTSIntroduction................................................................................................................................................. 3I. TERMS AND NOTATION....................................................................................................................... 5II. GROUPOIDS AND CATEGORIES...................................................................................................... 61. The notion of groupoid......................................................................................................................... 62. Equivalence of the definition of groupoid to the definition of Ehresmann.................................. 83. Relationship between l.lio notion of an liliroHiminn groupoid and the notion of a Brandt,groupoid...................................................................................................................................................... 94. Categories of functions and representation theorems................................................................. 125. The algebraic product of sets and the closure of a sot in the multiplicative system............... 15III. THE RELATIONSHIP BETWEEN A GOŁĄB PSEUDOOROUP AND AN EHRESMANN GROUPOID............................................................................................................... 166. The notions of a Gołąb pseudogroup and of a functional element............................................ 167. The isomorphism of an arbitrary Ehresmann groupoid and a Gołąbpseudogroup of a certain type. Groupoids of functional elements................................................. 18IV. GENERATING IN GOŁĄB PSEUDOGROUPS AND SOME PROPERTIES OF A SET OF FUNCTIONS.............................................................................................................................. 208. Some operations with sets of functions........................................................................................... 219. A quasi-order of the family of all subsets of the set, L (X)............................................................. 2410. Determining a pseudogroups with the aid of sets of functional elements............................. 2611. The problom of the existence of the smallest pseudogroup including a given setof local homeomorphisms...................................................................................................................... 29V. SEMI-PSEUDOGROUPS AND A GENERALIZATION OP THE NOTION OF AN ANALYTICAL STRUCTURE................................................................................................................ 3312. Semi-pseudogroups......................................................................................................................... 3313. The notion of an analytical structure............................................................................................... 35References................................................................................................................................................. 39

How to cite

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W. Waliszewski. Categories, groupoids, pseudogroups and analytical structures. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1965. <http://eudml.org/doc/268463>.

@book{W1965,
abstract = {CONTENTSIntroduction................................................................................................................................................. 3I. TERMS AND NOTATION....................................................................................................................... 5II. GROUPOIDS AND CATEGORIES...................................................................................................... 61. The notion of groupoid......................................................................................................................... 62. Equivalence of the definition of groupoid to the definition of Ehresmann.................................. 83. Relationship between l.lio notion of an liliroHiminn groupoid and the notion of a Brandt,groupoid...................................................................................................................................................... 94. Categories of functions and representation theorems................................................................. 125. The algebraic product of sets and the closure of a sot in the multiplicative system............... 15III. THE RELATIONSHIP BETWEEN A GOŁĄB PSEUDOOROUP AND AN EHRESMANN GROUPOID............................................................................................................... 166. The notions of a Gołąb pseudogroup and of a functional element............................................ 167. The isomorphism of an arbitrary Ehresmann groupoid and a Gołąbpseudogroup of a certain type. Groupoids of functional elements................................................. 18IV. GENERATING IN GOŁĄB PSEUDOGROUPS AND SOME PROPERTIES OF A SET OF FUNCTIONS.............................................................................................................................. 208. Some operations with sets of functions........................................................................................... 219. A quasi-order of the family of all subsets of the set, L (X)............................................................. 2410. Determining a pseudogroups with the aid of sets of functional elements............................. 2611. The problom of the existence of the smallest pseudogroup including a given setof local homeomorphisms...................................................................................................................... 29V. SEMI-PSEUDOGROUPS AND A GENERALIZATION OP THE NOTION OF AN ANALYTICAL STRUCTURE................................................................................................................ 3312. Semi-pseudogroups......................................................................................................................... 3313. The notion of an analytical structure............................................................................................... 35References................................................................................................................................................. 39},
author = {W. Waliszewski},
keywords = {topology},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Categories, groupoids, pseudogroups and analytical structures},
url = {http://eudml.org/doc/268463},
year = {1965},
}

TY - BOOK
AU - W. Waliszewski
TI - Categories, groupoids, pseudogroups and analytical structures
PY - 1965
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction................................................................................................................................................. 3I. TERMS AND NOTATION....................................................................................................................... 5II. GROUPOIDS AND CATEGORIES...................................................................................................... 61. The notion of groupoid......................................................................................................................... 62. Equivalence of the definition of groupoid to the definition of Ehresmann.................................. 83. Relationship between l.lio notion of an liliroHiminn groupoid and the notion of a Brandt,groupoid...................................................................................................................................................... 94. Categories of functions and representation theorems................................................................. 125. The algebraic product of sets and the closure of a sot in the multiplicative system............... 15III. THE RELATIONSHIP BETWEEN A GOŁĄB PSEUDOOROUP AND AN EHRESMANN GROUPOID............................................................................................................... 166. The notions of a Gołąb pseudogroup and of a functional element............................................ 167. The isomorphism of an arbitrary Ehresmann groupoid and a Gołąbpseudogroup of a certain type. Groupoids of functional elements................................................. 18IV. GENERATING IN GOŁĄB PSEUDOGROUPS AND SOME PROPERTIES OF A SET OF FUNCTIONS.............................................................................................................................. 208. Some operations with sets of functions........................................................................................... 219. A quasi-order of the family of all subsets of the set, L (X)............................................................. 2410. Determining a pseudogroups with the aid of sets of functional elements............................. 2611. The problom of the existence of the smallest pseudogroup including a given setof local homeomorphisms...................................................................................................................... 29V. SEMI-PSEUDOGROUPS AND A GENERALIZATION OP THE NOTION OF AN ANALYTICAL STRUCTURE................................................................................................................ 3312. Semi-pseudogroups......................................................................................................................... 3313. The notion of an analytical structure............................................................................................... 35References................................................................................................................................................. 39
LA - eng
KW - topology
UR - http://eudml.org/doc/268463
ER -

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