REPRESENTATION THEORY AND AUTOMORPHIC FORMS
CONTENTS CARDINAL AND ORDINAL NUMBERS COUNTABLE SETS ORDER OF IN?NITY THE AXIOM OF CHOICE MORE ON EQUINUMEROSITY ARITHMETIC OF CARDINAL NUMBERS WELL-ORDERED SETS TRANS?NITE INDUCTION ORDINAL NUMBERS ALEPHS 1 10 TREES 1 11 INDUCTION ON TREES 1 12 THE SOUSLIN OPERATION 1 13 IDEMPOTENCE OF THE SOUSLIN OPERATION TOPOLOGICAL PRELIMINARIES METRIC SPACES POLISH SPACES COMPACT METRIC SPACES MORE EXAMPLES THE BAIRE CATEGORY THEOREM TRANSFER THEOREMS STANDARD BOREL SPACES MEASURABLE SETS AND FUNCTIONS BOREL-GENERATED TOPOLOGIES THE BOREL ISOMORPHISM THEOREM MEASURES CATEGORY BOREL POINTCLASSES ANALYTIC AND COANALYTIC SETS PROJECTIVE SETS 1 COMPLETE SETS REGULARITY PROPERTIES THE FIRST SEPARATION THEOREM ONE-TO-ONE BOREL FUNCTIONS THE GENERALIZED FIRST SEPARATION THEOREM BOREL SETS WITH COMPACT SECTIONS POLISH GROUPS REDUCTION THEOREMS 4 10 CHOQUET CAPACITABILITY THEOREM 4 11 THE SECOND SEPARATION THEOREM 4 12 COUNTABLE-TO-ONE BOREL FUNCTIONS SELECTION AND UNIFORMIZATION THEOREMS PRELIMINARIES KURATOWSKI AND RYLL-NARDZEWSKI’S THEOREM DUBINS – SAVAGE SELECTION THEOREMS PARTITIONS INTO CLOSED SETS VON NEUMANN’S THEOREM A SELECTION THEOREM FOR GROUP ACTIONS BOREL SETS WITH SMALL SECTIONS BOREL SETS WITH LARGE SECTIONS PARTITIONS INTO G? SETS 5 10 RE?ECTION PHENOMENON 5 11 COMPLEMENTATION IN BOREL STRUCTURES 5 12 BOREL SETS WITH ?-COMPACT SECTIONS 5 13 TOPOLOGICAL VAUGHT CONJECTURE 5 14 UNIFORMIZING COANALYTIC SETS COUNTABLE SETS TWO SETS A AND B ARE CALLED EQUINUMEROUS OR OF THE SAME CARDINALITY, WRITTEN A ?B, IF THERE EXISTS A ONE-TO-ONE MAP F FROM A ONTO B SUCH AN F IS CALLED A BIJECTION FOR SETS A, B, AND C WE CAN EASILY CHECK THE FOLLOWING A ?A, A ?B =?B ?A, AND (A ?B & B ?C) =?A ?C 1THESE ARE PRODUCED HERE FROM MY ARTICLE [117] WITH THE PERMISSION OF THE INDIAN ACADEMY OF SCIENCES