I was looking for a particular book on Topology, however I forgot the author name. I had asked my instructor how to find HOMEOMORPHIC classes between the symbols $N, B, H$ & $M.$ Then my professor hinted me with $X$ and $Y$. He told me that If I remove a point from $X$, I can get $4 $ disjoint connected components from it however it does not happen with $ Y, $ In the same way, so they are not homeomorphic. Later he asked me to solve the orignal problem. Later on he told me that during his PhD, He had read a Topology book, in which the orignal author asks us to find homeomorphic sets from $A, B, C, D...... Z.$
Can anyone tell me the name of that book? He also told me that the book is interesting but the problems are very challenging.. Does anyone have any idea about which book he was talking about?
Choquet, in Topology (Academic Press, 1966) appears to have originated the problem as an exercise (in Chapter 1, p.21), but I can't rule out that it wasn't folklore earlier, or that someone else originated it and Choquet just made it more available. Choquet's book is definitely both interesting and challenging, moreso these days because some of the notational practices have changed.
If you're interested more in how to determine which letters of the alphabet are homeomorphic to which others, then there's a paper by Lopez (https://arxiv.org/pdf/1410.3364.pdf ) which covers it rather nicely and refers to Choquet as well.