An Introduction To General Topology Paul E Long Pdf Link May 2026

Write-up:

General topology, also known as point-set topology, is a branch of mathematics that deals with the study of topological properties of spaces. It is a fundamental area of mathematics that has numerous applications in analysis, algebra, geometry, and other fields. "An Introduction to General Topology" by Paul E. Long is a comprehensive textbook that provides an introduction to the basic concepts and principles of general topology.

The book covers the fundamental topics of general topology, including point-set topology, topological spaces, continuous functions, compactness, connectedness, and separation axioms. The author presents the material in a clear and concise manner, making it easy for readers to understand and follow. The book also includes numerous examples, exercises, and illustrations to help readers develop their problem-solving skills and deepen their understanding of the subject.

Book Information:

Title: An Introduction to General Topology Author: Paul E. Long Publisher: Prentice Hall Year: 1971 Pages: 244 an introduction to general topology paul e long pdf link

PDF Link:

Unfortunately, I couldn't find a publicly available PDF link for the book. However, you can try searching for the book on online libraries or academic databases such as:

• Google Books: https://books.google.com
• Amazon: https://www.amazon.com
• Academia.edu: https://academia.edu
• ResearchGate: https://www.researchgate.net

You can also try checking online libraries or requesting the book through interlibrary loan services.

Alternative Resources:

If you're looking for alternative resources to learn general topology, here are some online resources:

• Topology Atlas: https://www.topologyatlas.com
• General Topology by Walter Rudin: https://www.math.wichita.edu/~jww/rudin.pdf
• Topology by James R. Munkres: https://www.math.uconn.edu/~kconrad/math5337s07/munkres.pdf

Chapter-by-Chapter Breakdown of Long’s Text

To understand why so many students hunt for an "introduction to general topology paul e long pdf link," let’s examine the structure:

• Chapter 1: Preliminaries – Sets, mappings, equivalence relations, countable and uncountable sets.
• Chapter 2: Topological Spaces – Definition via open sets, closed sets, neighborhood systems, and bases (with many concrete examples: metric spaces, discrete/indiscrete, finite complement, and order topologies).
• Chapter 3: Continuity and Homeomorphisms – ε-δ generalization, sequential continuity, open/closed maps.
• Chapter 4: Product and Quotient Spaces – Finite and infinite products (box vs. product topology), identification spaces.
• Chapter 5: Separation Axioms – T0 through T4, Urysohn lemma (stated and used), Tietze extension theorem (briefly).
• Chapter 6: Compactness – Heine-Borel generalization, countable compactness, sequential compactness, Bolzano-Weierstrass property.
• Chapter 7: Connectedness – Connected and path-connected components, local connectedness.
• Chapter 8: Completeness (in metric spaces) – Completion of a metric space, Baire category theorem.

Chapter 1: Sets and Functions

A concise review of set theory, including De Morgan’s laws, relations, functions, and the axiom of choice. Long assumes the reader has mathematical maturity but provides a safety net.

Who is Paul E. Long?

Paul E. Long was a professor of mathematics at the University of Arkansas. Unlike celebrity authors like Munkres or Kelley, Long wrote primarily for the undergraduate who finds topology intimidating. His teaching philosophy revolved around clarity, incremental difficulty, and a "no-frills" approach. An Introduction to General Topology (published by Charles E. Merrill, later reprinted by Dover Publications) reflects this philosophy perfectly. It is concise (around 200 pages), affordable, and laser-focused on core concepts. Google Books: https://books

Chapter 3: Basis for a Topology

Here, Long introduces the concept of a basis—a efficient way to generate a topology. This leads naturally to the product topology and the subspace topology. His treatment of the product topology is particularly clear, using projection mappings.

Chapter 4: Continuity and Homeomorphism

Long redefines continuity in purely topological terms (the preimage of an open set is open). He then introduces homeomorphisms—the notion of equivalence for topological spaces. The chapter includes classic problems: proving that (0,1) is homeomorphic to R, and that a circle is not homeomorphic to an interval.

What Makes This Book Unique?

In a crowded field of topology textbooks, Long’s work stands out for three reasons:

1. Brevity without Sacrifice – Where Munkres takes 500+ pages, Long covers all essential topics (topological spaces, continuity, separation axioms, compactness, connectedness, product spaces, and quotient spaces) in under 250 pages.
2. Exceptional Exercises – The book contains over 500 problems, ranging from routine verifications to challenging proofs that foreshadow advanced topics (e.g., Tychonoff’s theorem is handled in the exercises).
3. Self-Contained Preliminaries – The first chapter reviews naive set theory, relations, functions, and cardinality, making it accessible to second-year undergraduates.