In the definition of a topology, the empty set and the whole space must be open. Solutions sometimes forget to explicitly verify these trivial cases in proofs about bases or subbases.
Simply having the is not enough. You must use them to build mathematical maturity. Here is a 5-step protocol: Introduction To Topology Mendelson Solutions
Mendelson’s Introduction to Topology remains a masterpiece of concise exposition. Its solutions—though unofficial—form a vital study aid, helping students bridge the gap between reading definitions and constructing rigorous proofs. Used wisely, a solutions guide transforms the book from a challenging monologue into a dialogue with the foundations of modern mathematics. In the definition of a topology, the empty
Some specific solutions to exercises in Mendelson's book include: In the definition of a topology
