
Recent Posts
Archives
 January 2012 (1)
 October 2011 (1)
 July 2011 (6)
 June 2011 (8)
 May 2011 (7)
Categories
 Analysis (9)
 Definition (2)
 Descriptive Set Theory (18)
 Kechris (17)
 Logic (3)
 Rudin RC (1)
 Topology (5)
 Metric Spaces (3)
 Separability (2)
 Uncategorized (2)
 Unsolved (1)
Meta
Category Archives: Metric Spaces
Questions
I have been unable to solve the following problems from Kechris. Any hints, advice, or solutions would be appreciated. 1. Exercise 4.9: Let be separable Banach spaces. The weak topology on is the one generated by the functions (from into … Continue reading
Posted in Analysis, Descriptive Set Theory, Kechris, Metric Spaces, Topology, Unsolved
2 Comments
A complete, compatible metric for the strong topology (p15 (A))
Let be separable Banach spaces over . Show that the following is a complete, compatible metric for the strong topology on : where is a dense sequence in the unit ball of . Proof. It is not difficult to check … Continue reading
Any subspace of a separable metric space is separable
Let be a separable, metric space, , and let be countable and dense. For each , choose if such intersection is nonempty. Then, is a countable subset of . Let . Then choose . Now, choose such that . Then, , so … Continue reading
Posted in Metric Spaces, Separability, Topology
Leave a comment