Frustrated by this one exercise
Can you help me on this problem please?
I tried searching online, but I cannot find the proof: In T_3 space (or regular and T_1 (any onepoint set is closed)), show that every prime zfilter is contained in a unique zultrafilter. I feel so stupid because I spent lots of time and I cannot still do it. 
Re: Frustrated by this one exercise
try telling us clearly what the words mean.

Re: Frustrated by this one exercise
zfilter is the collection F of nonempty zero sets (f^{1}(0) of continuous f:X > I) such that
a) P_1, P_2 in F implies P_1 intersection P_2 in F b) P_1 in F and a zero set P_2 containing P_1 implies P_2 in F. A zfilter is prime if P_1 and P_2 belong to set of zero sets and P_1 union P_2 in F, then P_1 is in F or P_2 is in F. An zultrafilter is a maximal zfilter. As this exercise is from Willard, T_3 means that it is regular and T_1 (where all single point sets are closed) 
All times are GMT 5. The time now is 06:42 AM. 
Powered by vBulletin Copyright ©2000  2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums