Recent content by skitzolala

Since X\setminus V_1 is closed in T1 it would be it's own closure. Hence it isn't dense in T1 so it can't be dense in T2.

I suppose you would assume that X\setminus V_1 is not dense hence the compliment of its closure can't be the empty set?

Okay, so V_1 is open in T1 implying that X\setminus V_1 is closed in T1. X\setminus V_1 \subset cl_2(X\setminus V_1) and hence the closure in T2 must share some elements with V1. Thus X\setminus cl_2(X\setminus V_1) \subset V_1 and X\setminus cl_2(X\setminus V_1) is open in T2. This seems solid...

Okay so now I would have, X\setminus cl_2(V_1) which is an open set in \tau_2 is either contained in or contains X\setminus cl_1(V_1) which is an open set in \tau_1? This seems right because either the closure in T1 has to be bigger or the closure in T2 has to be but where does denseness come...

Homework Statement The problem is as follows: Homework Equations We are using the definition that D is dense if its closure is the whole space. Proofs using this definitions would be best as we were not taught any equivalent ones. Not sure if relevant but just in case: ~ is an...