The heart of the introduction. Long defines a topology, open sets, closed sets, and the axioms (the empty set and whole space are open; finite intersections and arbitrary unions of open sets are open). He provides numerous examples: the discrete topology, indiscrete topology, finite complement topology, and the usual topology on the real line.
While waiting to obtain Long’s PDF, consider legal, free topology texts:
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.
The book was originally published in 1971. However, Dover Publications released an inexpensive paperback reprint (ISBN-10: 0486836572, ISBN-13: 978-0486836571). Dover owns the current copyright. As such, no legal, free PDF is distributed by the publisher or author. You will find many random PDF hosting sites (e.g., academia.edu, archive.org, or libgen) offering downloads—these are almost always copyright violations unless the copy is explicitly marked as out of copyright (it is not, because Dover’s edition is from 2019). an introduction to general topology paul e long pdf link
Absolutely. While newer textbooks (Munkres, 2nd ed.) include category theory and algebraic topology, Long’s focus on general topology remains timeless. Many graduate entrance exams (e.g., GRE Math Subject Test) cover topics exactly as Long presents them.
The exercises in Long are legendary among professors—they are not overly computational but deeply theoretical. For example:
These are not merely textbook drills; they are the building blocks of research-level analysis. The heart of the introduction
Long’s text is ideal for: – Mathematics undergraduates taking their first topology course after real analysis. – Graduate students in engineering or physics needing a quick, rigorous overview. – Self-learners who have completed a proof-based linear algebra or advanced calculus course. – Instructors seeking a source of clean, non-trivial homework problems.
It is not recommended for those needing a thorough treatment of algebraic topology (homotopy, homology) or set-theoretic topology beyond the basics.
If you acquire a legal copy (PDF or physical), follow this study plan: These are not merely textbook drills; they are
| Textbook | Difficulty | Length | Cost | Best For | |----------|------------|--------|------|----------| | Munkres, Topology (2nd ed.) | High | 537 pp | $70–150 | Grad school bound | | Kelley, General Topology | Very high | 320 pp | $60–120 | Advanced grad | | Long, An Introduction to General Topology | Medium | 200 pp | $15–20 | Undergraduates, self-learners | | Morris, Topology Without Tears | Low-medium | 400 pp | Free | True beginners |
Long’s advantage is price-to-content ratio. For under $20, you get a rigorous, proof-heavy topology core.