The famous hierarchy: ( T_0, T_1, T_2 ) (Hausdorff), regular (( T_3 )), and normal (( T_4 )) spaces. Long explains why Hausdorff spaces are essential for uniqueness of limits and why normal spaces are required for Urysohn’s metrization theorem (introduced later in exercises).
For decades, students transitioning from advanced calculus to abstract mathematics have faced a notorious gatekeeper: General Topology. Often called "point-set topology," this subject forms the bedrock of modern analysis, geometry, and even functional analysis. Among the many textbooks available, one consistently underrated gem is An Introduction to General Topology by Paul E. Long.
If you have searched for the phrase "an introduction to general topology paul e long pdf link," you are likely a mathematics student, an instructor looking for supplementary materials, or a self-learner wanting a clear, exercise-driven text without breaking the bank. This article will provide a detailed review of Long’s book, discuss its unique place in the literature, and—most importantly—guide you on legitimate ways to access the PDF while respecting copyright laws.
| Textbook | Difficulty | Length | Emphasis | Best For | | :--- | :--- | :--- | :--- | :--- | | Long | Intermediate | ~200 pages | Concise, exercise-heavy | One-semester undergrad course | | Munkres | Advanced | 500+ pages | Comprehensive, includes algebraic topology | Grad school preparation | | Kelley | Expert | ~300 pages | General topology for analysts | Math graduate students | | Morris (free) | Beginner | ~400 pages | Accessible, conversational | Self-learners without a professor | an introduction to general topology paul e long pdf link
Long occupies a unique sweet spot: shorter than Munkres, harder than Morris, and more approachable than Kelley.
If you have obtained (or plan to obtain) a legitimate copy, here is how to succeed:
If your local library doesn’t own the book, request an ILL. They will scan the entire book (often as a PDF) and send it to you for free or a nominal fee. This is 100% legal. The famous hierarchy: ( T_0, T_1, T_2 )
Pearson Education occasionally sells legacy titles as print-on-demand. Check Pearson’s official site. Alternatively, buy a used physical copy from AbeBooks or ThriftBooks (often under $20) and scan it yourself.
About the Book
Paul E. Long’s An Introduction to General Topology is a well-regarded, upper-undergraduate level textbook. It strikes a balance between rigorous proof-based mathematics and clear exposition. Compared to heavier classics like Munkres or Kelley, Long’s book is often praised for being more accessible to a first-time learner while still covering essential topics thoroughly. Why students look for this book:
Typical topics covered:
Why students look for this book:
The book is structured into eight core chapters, each building logically upon the last.