Answers to Burt Mendelson's text - "Introduction to topology - third edition"

I was reading this book and thought it would be a good idea to provide answers to it. I added a few questions myself. These were either based on proofs shown in the text, proofs left to the reader, or proofs I used myself to clarify things.

My proof style will probably change as you read through the text. This is inevitable because I should have became more advanced in skill as I practiced more and progressed through the text. And in anycase, my proof style tends to change with my mood.

The nature of the questions are that it is generally clear to the proponent if he is correct or not, since the arguments which are the substance of a proof speak for themselves, in which case the need for a set of answers seems lacking. Nethertheless, perhaps the answers can serve a struggling student who needs extra clarification (and instead will end up with their mind boggled by my convoluted proofs), or perhaps the student desires a different perspective. In any case, reading and checking proofs is always a good exercise.

If you spot that I have made a mistake, please let me know and I will endeavor to correct it. In the case of you spotting a typo, your name will be listed in an appended section entitled "Typo Spotters". In the case of you spotting an error, I expect you to provide an alternative, correct proof. I will then attempt to excise my stupidity with my own alternative correct proof. Both your proof and my alternative proof will occur in the text, my proof will follow yours, and your name will occur in the text at the point of your proof (unless you wish to remain anonymous) accompanied by an acknowledgement that I made a mistake (this should incite me to double check my proofs the first time round).

Enjoy yourself doing the questions.