Well, my good friend Kelvin Tan has been bugging me to blog! So I am going to entertain him with a post that he would probably not understand! Then again, I don't think I will understand it either! Anwyay, U-liang blogged about his Honours Project, so I thought I wrote a bit about mine as well, so as to let you peeps out there know what kind of trouble I've gotten myself into!
A tale of 2 spaces, that is the project title given to me by my supervisor A/P Denny Leung (who in my opinion is one of the best lecturers in the NUS math dept). The project is categorised under topology, geometry and analysis. So, I would think that most people, who are in their correct frame of mind, would avoid this project at all cost!
Back to the point, the scope of the project is to characterize certain topological properties of the Cantor Space and the Baire Space. Both of which have interesting properties that make them useful in mathematics.
What I have accomplished so far. Well, I have spent the past week reviewing some results and theorems from metric spaces. But after taking MA4211 and MA4262 (you can read about them in my April archive) I don't think there is really much to review. Also started to read up a bit on topology, which is actually quite interesting, but not what I expected. Now I know why the wolfram website characterizes analysis and topology as seperate branches in mathematics.
Yesterday was a pretty good day (or so I thought). A brain wave suddenly hit me and was able to write down what I thought was a satisfactory proof to one of the ten results that I needed to proof. Oh well, seems that I made quite a huge oversight and did not consider something pretty important to the result. Well, only goes to show that I need to relook that whole proof all over again. But well, it's an interesting project so far!
So, Rev Tan.. happy!?!?! (You can try asking your girlfriend to translate for you! If she understands!)
