Is it rude to change universities/supervisors after already indicating research interest with a current supervisor? I am currently an undergraduate student studying in an area of mathematics and am planning to apply to do a masters research degree next year. I have been doing research with my supervisor who works in some topic say X and will be doing more research throughout the remainder of the year with him.

I am still very interested in topic X and consider this a large option for my masters, however, I have greater interests in another topic say Y. There is another university in our country that has a specialist research group in topic Y. I am looking into changing to this alternative university to study topic Y for my masters, however, I have had no conversations about my future research with people at either university.

Would it be considered rude for me to leave my supervisor now, who currently offers me a lot of support during my undergraduate, to pursue research in this other area of mathematics solely because I am more interested in this alternative topic? And what would be the correct way to go about this without burning any bridges with my current supervisor?
If Y is what you really want to do then go for it. There is no point in going down a career path just to please someone else.

Talk in person to your current supervisor once you have a written offer from the university that does Y. Explain to him that it is your dream to do Y and you hope to keep in contact with him even though you are leaving the university.

A good supervisor will understand - if not then he was not a good supervisor anyway. It's a win-win for you.