If you search for "General Topology Problem Solution Engelking" on academic platforms, you will find three types of resources:

Engelking assumes a high level of mathematical maturity. Problems frequently rely on set theory (Zorn's Lemma, ordinal numbers, cardinal arithmetic) as if it were second nature to the reader. If your set theory is rusty, the topology problems will feel impossible, not because of the topology, but because of the foundations.

Let ( X ) be a topological space, ( A \subset X ). Prove that ( \partial (\partial A) \subset \partial A ). Find an example where ( \partial (\partial A) \neq \partial A ).

exists. Engelking deliberately omitted detailed solutions; the book is a reference, not a textbook with answers.

cap A equals f to the negative 1 power of open paren cap U close paren space and space cap B equals f to the negative 1 power of open paren cap V close paren are open in , their preimages are open sets in 4. Show the partition of the domain We now check the relationship between within the space are non-empty subsets of , there must be points in that map to them. Thus, : If there were a point would be in . However, must map to either . Therefore, 5. Reach a contradiction We have shown that can be partitioned into two non-empty, disjoint open sets . By definition, this means disconnected . However, this contradicts our initial assumption that is connected.