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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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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