- #1
Math Amateur
Gold Member
MHB
- 3,990
- 48
I am reading D. J. H. Garling: "A Course in Mathematical Analysis: Volume I Foundations and Elementary Real Analysis" ... ...
At present I am focused on Chapter 1: The Axioms of Set Theory and need some help with Theorem 1.2.2 and its relationship to the Separation Axiom ... ...
The Separation Axiom and Theorem 1.2.2 read as follows:
Garling argues that the Separation Axiom needs to be in place before we can prove Theorem 1.2.2 ... ... but I cannot see where the Separation Axiom is needed in the proof of Theorem 1.2.2 ...
Can someone give a clear explanation of exactly why we need the Separation Axiom in order to prove Theorem 1.2.2.
Help will be much appreciated ... ...
Peter
At present I am focused on Chapter 1: The Axioms of Set Theory and need some help with Theorem 1.2.2 and its relationship to the Separation Axiom ... ...
The Separation Axiom and Theorem 1.2.2 read as follows:
Can someone give a clear explanation of exactly why we need the Separation Axiom in order to prove Theorem 1.2.2.
Help will be much appreciated ... ...
Peter