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Math and science::Topology

Connectedness Examples

  • \( X = \mathbb{R} \setminus \{0\} \) is [something about connectedness].
  • The space of rationals numbers \( \mathbb{Q} \), topologized as a subspace of \( \mathbb{R} \), is [something about connectedness].
  • A discrete space with 2 or more points is [something about connectedness].
  • A non-empty indiscrete space is [something about connectedness].
  • An interval topologized as a subspace of \( \mathbb{R} \) is [something about connectedness].
  • The space \( \mathbb{R}^d \) is [something about connectedness].
  • The letter 'O' is [something about connectedness].
  • The collection of connected sets in \( \mathbb{R} \) coincide preciesly with [...].