Definition
A topological space is connected if it is not a union of two non-empty open sets.
i.e. if you draw the two non-empty open sets on the graph, if you have to lift your pen, it will not be connected.
Examples
Not connected:
Connected:
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A topological space is connected if it is not a union of two non-empty open sets.
i.e. if you draw the two non-empty open sets on the graph, if you have to lift your pen, it will not be connected.
Not connected:
⟨0,1]∪[2,5⟩
Connected:
⟨0,1]∪[0.5,5⟩=⟨0,5⟩