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by nhatcher
876 days ago
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Non locally connected spaces are a bit pathological. Means that given a point there is always a neighborhood of the point (might be very small) that is connected.
An example of a connected but not locally connected is:
https://en.m.wikipedia.org/wiki/Topologist%27s_sine_curve
From (0, O) any neighborhood, no matter how small contains points that belong to the curve but cannot reach (0, 0) and stay in the neighborhood. |
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