home3 - MATH 7338 HOMEWORK #3 Due date: October 29, 2009...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 7338 HOMEWORK #3 Due date: October 29, 2009 Work FIVE of the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected for grading. Write LEGIBLY on the FRONT side of the page only, and STAPLE your pages together. 1. Let F ( R ) be the vector space containing all functions f : R C . For each x R , define a seminorm on F ( R ) by x ( f ) = | f ( x ) | . Then convergence with respect to the family of seminorms { x } x R corresponds to pointwise convergence of functions. Show that this topology is not normable, i.e., Show that there is no norm on F ( R ) that defines the same convergence criterion. Hint: Find f n such that c n f n 0 pointwise for every choice of scalars c n . 2. Let { } J be a family of seminorms on a vector space X. Show that the induced topology on X is Hausdorff if and only if ( x ) = 0 for all...
View Full Document

This note was uploaded on 08/25/2011 for the course MATH 7338 taught by Professor Heil during the Fall '09 term at Georgia Institute of Technology.

Page1 / 2

home3 - MATH 7338 HOMEWORK #3 Due date: October 29, 2009...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online