I have been studying Singer/Thorpe's Lecture Notes in Topology and Geometry as a brief introduction to topology and algebraic topology before reading books like Engelking's General Topology and Massey, Spanier, and Hatcher's books in the algebraic topology. I noticed that S/T has very few problems to work, which are not suitable....

Could you recommend me some sources (books, websites, etc.) that accompany S/T for problem sets?

  • $\begingroup$ Engelking's General Topology has a very large collection of exercises and problems ranging from easy to deep. Many of them are to cover additional results which, if they were all presented in the body of the text, would make the book ridiculously large. Examples: (1). A space $S$ is $T_3$ iff whenever $p\in U\subset S$ and $U$ is open, there exists open $V$ with $p\in V\subset \bar V\subset U.$.. (2). When $C$ is a closed subset of a metric space $X ,$ any continuous $f:C\to \mathbb R$ can be extended to a continuous $f^*:X\to \mathbb R.$ $\endgroup$ – DanielWainfleet Aug 19 '16 at 3:46

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