• $$X = \mathbb{R} \setminus \{0\}$$ is [something about connectedness].
• The space of rationals numbers $$\mathbb{Q}$$, topologized as a subspace of $$\mathbb{R}$$, is [something about connectedness].
• An interval topologized as a subspace of $$\mathbb{R}$$ is [something about connectedness].
• The space $$\mathbb{R}^d$$ is [something about connectedness].
• The collection of connected sets in $$\mathbb{R}$$ coincide preciesly with [...].