(a) Show that a collection {(-∞, q) C R | q is rational } is a basis for a topology on R.(b) Show this basis generates the same topology on R as the topology in Homework 2 problem(4).

Since for your B part there is no information regarding the topology homework 2 problem 4. Hence if…

Answered: Show that a collection {(-∞,q) C R | q…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...

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Show that a collection {(-∞,q) C R | q is rational } is a basis for a topology on R.