Topologies

Geometry Level 3

Which of the following collections T \mathcal T of subsets of R\mathbb R is a topology on R\mathbb R?

I. T= \mathcal T = the empty set, R\mathbb R, and all intervals of the form [a,) [a,\infty) for any aR a \in \mathbb R
II. T=\mathcal T = the empty set, plus all subsets YR Y \subseteq \mathbb R such that the complement RY{\mathbb R} \setminus Y is finite
III. T=\mathcal T = the empty set, plus all infinite subsets YRY \subseteq \mathbb R

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