\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For each of the following, determine whether it is a neighborhood of \(a\) in the given ambient space.
  1. \(V = \,]0, +\infty[\,\), \(a = 1\), in \(\mathbb{R}\).
  2. \(V = \,]0, +\infty[\,\), \(a = 0\), in \(\mathbb{R}\).
  3. \(V = \mathbb{R}\), \(a = 1\), viewed inside \(\mathbb{C}\).
  4. \(V = \{z \in \mathbb{C} : \operatorname{Re}(z) > 0\}\), \(a = 1\), in \(\mathbb{C}\).

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