Let C be an arbitrary non-empty set in Rn. With a given number R and
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Question:
Let C be an arbitrary non-empty set in Rn. With a given number α ∈ R and α ̸= 0 (i.e., the number α is fixed and does not change), we can define another set αC as follows:
\alpha C := {y \epsilon R^/^n | y = \alpha x, for some x \epsilon C}
For all the questions below, you must provide rigorous arguments to support your answer.
1. Is αC Convex?
2. Is αC a cone?
3. Now suppose that set C is convex, is αC Convex?
4. If the set C is a cone (regardless convex or not), is Is αC a cone?
Related Book For
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
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