This book is a systematic exposition of the part of general topology which has proven useful in several branches of mathematics.It is especially intended as background for modern analysis,and I have,with difficulty,been prevented by my friends from labeling it: What Every Young Analyst Should Know.

CNAPTER 0:PRELIMINARIES

 SETS

 SUBSETS AND COMPLEMENTS;UNION AND INTERSECTION

 RELATIONS

 FUNCTIONS

 ORDERINGS

 ALGEBRAIC CONCEPTS

 THE REAL NUMBERS

 COUNTABLE SETS

 CARDINAL NUMBERS

 ORDINAL NUMBERS

 CARTESIAN PRODUCTS

 HAUSDORFF MAXIMAL PRINCIPLE

CNAPTER 1:TOPOLOGICAL SPACES

 TOPOLOGIES AND NEIGHBORHOODS

 CLOSED SETS

 ACCUMULATION POINTS

 CLOSURE

 INTERIOR AND BOUNDARY

 BASES AND SUBBASES

 RELATIVIZATION;SEPARATION

 CONNECTED SETS

 PROBLEMS

CNAPTER 2:MOORE-SMITH CONVERGENCE

 INTRODUCTION

 DIRECTED SETS AND NETS

 SUBNETS AND CLUSTER POINTS

 ……

CNAPTER 3:PRODUCT AND QUOTIENT SP ACES

CNAPTER 4:EMBEDDING AND METRIZATION

CNAPTER 5:COMPACT SPACES

CNAPTER 6:UNIFORM SPACES

CNAPTER 7:FUNCTION SPACES

APPENDIX:ELEMENTARY SET THEORY

INDEX