Please please solve with clear explanation 1. (a) Let f: X → R be a subadditive function defined on a topological vector space. Prove that iff is continuous at xo = 0, then it is continuous on X.(b) Let 2 be a convex set in a topological vector space X such that 0 € int(N). Prove that theMinkowski function po associated with 2 is continuous.D.

As you have asked more than one different/unreated to each other questions. We shall solve first…

Answered: 1. (a) Let f: X → R be a subadditive…

1. (a) Let f: X → R be a subadditive function defined on a topological vector space. Prove that if f is continuous at To = 0, then it is continuous on X.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...

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Question

Please please solve with clear explanation

1. (a) Let f: X → R be a subadditive function defined on a topological vector space. Prove that if
f is continuous at xo = 0, then it is continuous on X.
(b) Let 2 be a convex set in a topological vector space X such that 0 € int(N). Prove that the
Minkowski function po associated with 2 is continuous.
D.

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