Before diving into abstract spaces, the book establishes a firm foundation in basic set theory. This includes an exploration of functions, relations, Cartesian products, and the indexing of families of sets. Understanding these concepts is critical, as topological structures are defined entirely using the language of sets. 2. Topological Spaces and Neighborhood Systems
While the full table of contents is not readily available online, library records indicate it follows a logical and comprehensive progression typical of a rigorous introduction to the topic. The book can be understood as building up from the most basic foundations:
The book was originally published in 1971. However, 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
The Internet Archive holds scanned, high-quality digital copies of thousands of mid-to-late 20th-century mathematics textbooks. Users can legally borrow An Introduction to General Topology digitally through their controlled digital lending program.
: A summary document covering definitions of topological spaces, connectedness, and separation axioms. Before diving into abstract spaces, the book establishes
Because the book was published in 1971, it predates the widespread digitization of academic texts. While this makes it a valuable classic, it also means it is less likely to have been officially scanned and released as a free PDF compared to a more modern open-access textbook.
: How to generate a topology from a smaller collection of subsets, a critical tool for constructing complex spaces. covering cartesian products
: The essential "alphabet" of topology, covering cartesian products, relations, and functions.
Paul E. Long’s An Introduction to General Topology remains a stellar benchmark for clear, deductive mathematical writing. Whether you find a physical copy or access a digital version through an academic archive, it will provide a rock-solid foundation for your mathematical journey.