Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered.
This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed.
This book is intended for students and teachers of mathematics.

Foreword to the First English EditionForeword to the Second English EditionPart I Set Theory Introduction to Part I I. Propositional Calculus § 1. The Disjunction and Conjunction of Propositions § 2. Negation § 3. Implication Exercises II. Algebra of Sets. Finite Operations § 1. Operations on Sets § 2. Inter-Relationship with the Propositional Calculus § 3. Inclusion § 4. Space. Complement of a Set § 5. The axiomatics of the Algebra of Sets § 6. Boolean Algebra. Lattices § 7. Ideals and Filters Exercises III. Propositional Functions. Cartesian Products § 1. The Operation {x: f(x)} § 2. Quantifiers § 3. Ordered Pairs § 4. Cartesian Product § 5. Propositional Functions of Two Variables. Relations § 6. Cartesian Products of n Sets. Propositional Functions of n Variables § 7. On the Axiomatics of Set Theory Exercises IV. The Mapping Concept. Infinite Operations. Families of Sets § 1. The Mapping Concept § 2. Set-Valued Mappings § 3. The Mapping Fx = {y: f(x,y)} § 4. Images and Inverse Images Determined by a Mapping § 5. The Operations ?R and nR. Covers § 6. Additive and Multiplicative Families of Sets § 7. Borel Families of Sets § 8. Generalized Cartesian Products Exercises V. The Concept of the Power of a Set. Countable Sets § 1. One-to-one Mappings § 2. Power of a Set § 3. Countable Sets Exercises VI. Operations on Cardinal Numbers. The Numbers a and c § 1. Addition and Multiplication § 2. Exponentiation § 3. Inequalities for Cardinal Numbers § 4. Properties of the Number c Exercises VII. Order Relations § 1. Definitions § 2. Similarity. Order Types § 3. Dense Ordering § 4. Continuous Ordering § 5. Inverse Systems, Inverse Limits Exercises VIII. Well Ordering § 1. Well Ordering § 2. Theorem on Transfinite Induction § 3. Theorems on the Comparison of Ordinal Numbers § 4. Sets of Ordinal Numbers § 5. The Number O § 6. The Arithmetic of Ordinal Numbers § 7. The Well-Ordering Theorem § 8. Definitions by Transfinite Induction ExercisesPart II Topology Introduction to Part II IX. Metric Spaces. Euclidean Spaces § 1. Metric Spaces § 2. Diameter of a Set. Bounded Spaces. Bounded Mappings § 3. The Hubert Cube § 4. Convergence of a Sequence of Points § 5. Properties of the Limit § 6. Limit in the Cartesian Product § 7. Uniform Convergence Exercises X. Topological Spaces § 1. Definition. Closure Axioms § 2. Relations to Metric Spaces § 3. Further Algebraic Properties of the Closure Operation § 4. Closed Sets. Open Sets § 5. Operations on Closed Sets and Open Sets § 6. Interior Points. Neighborhoods § 7. The Concept of open Set as the Primitive Term of the Notion of Topological Space § 8. Base and Subbase § 9. Relativization. Subspaces § 10. Comparison of Topologies § 11. Cover of a Space Exercises XI. Basic Topological Concepts § 1. Borel Sets § 2. Dense Sets and boundary Sets § 3. T1-spaces, T2-spaces § 4. Regular Spaces, Normal Spaces § 5. Accumulation Points. Isolated Points § 6. The Derived Set § 7. Sets Dense in Themselves Exercises XII. Continuous Mappings § 1. Continuity § 2. Homeomorphisms § 3. Case of Metric Spaces § 4.