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[0HM] Let’s consider on \(ℝ\) the family \(Ο„_+ =\{ (a, +∞) : a ∈ ℝ\} βˆͺ \{ βˆ…, ℝ\} \). Show that it is a topology. Is it Hausdorff? Calculate closure, interior, boundary and derivative of these sets:

\begin{align*} \{ 0\} \quad ,\quad \{ 0,1\} \quad ,\quad [0,1] \quad ,\quad (0,1) \quad ,\\[0,∞) \quad ,\quad (-∞,0] \quad ,\quad (0,∞) \quad ,\quad (-∞,0) \quad . \end{align*}

Solution 1

[0HN]

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Authors: "Mennucci , Andrea C. G." .
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  • space, topological
  • topological space
  • interior
  • closure
  • boundary
  • derivative
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