How to Prove a Set of Functions is Closed Under Addition (Example with functions s.t. f(0) = 0)

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SOLVED: Suppose that f(c) is a real-valued continuous function on [0,1]. Define addition on C by the unusual rule (f ⊕ g)(x) = max(f(x), g(x)), for f,g ∈ C and x ∈ [

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general topology - Topological spaces in which a set is the support of a continuous function iff it is the closure of a open set. - Mathematics Stack Exchange

a) Prove that with the operations of addition and

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Show the Set of Functions such that f(0) = 1 is Not Closed Under Addition

Solved Determine whether the subset of C(-o, ) is a subspace

Show the Set of Functions such that f(0) = 1 is Not Closed Under Addition

Closure Under Addition (Sets of Whole Numbers)

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Solved Let F be the set of all real-valued functions with

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