Can I use the usual three conditions to show that is a subspace. But how would that show that is a subspace of specifically ?
Is continuous functions with compact support? If so, then what particularly are you having trouble with, you know that the sum of two continuous functions is continuous as is the product of a continuous function by a scalar, thus it suffices to prove that the same is true for functions with compact support. But, it's clear that and so that is a closed subspace of and since this superset is compact it follows that is compact.