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A pseudo-arc is an example of a compact connected subset of the plane that is totally path-disconnected. If you allow examples in $\mathbb{R}^3$ rather than $\mathbb{R}^2$, another example is a solenoid.
A pseudo-arc is an example of a compact connected subset of the plane that is totally path-disconnected. If you allow examples in $\mathbb{R}^3$ rather than $\mathbb{R}^2$, another example is a solenoid.
A pseudo-arc is an example of a compact connected subset of the plane that is totally path-disconnected.
A pseudo-arc is an example of a compact connected subset of the plane that is totally path-disconnected. If you allow examples in $\mathbb{R}^3$ rather than $\mathbb{R}^2$, another example is a solenoid.
