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Decide if each of the following is a subspace

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The material is from ABSTRACT VECTOR SPACE.
Please kindly show each step of your solution.

(The material is from ABSTRACT VECTOR SPACE.
Please solve for parts (b) & (d).
means the space of the collection of continuous functions on R which is differentiable 0 time. Please explain each step of your solution sufficiently. Thank you.)

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Abstract vector space material is analyzed. Continuous functions on R which is differentiable is determined.

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