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David White
David White
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Assume that $X$ is a path-wise connected Hausdorff space, and asuumeassume that its fundamental group is non-trivial. Does it always exist a simple curve in $X$ which is non-null-homotopic?

Such curve does exist if we further assume that $X$ possesses a universal cover.

Assume that $X$ is a path-wise connected Hausdorff space, and asuume that its fundamental group is non-trivial. Does it always exist a simple curve in $X$ which is non-null-homotopic?

Such curve does exist if we further assume that $X$ possesses a universal cover.

Assume that $X$ is a path-wise connected Hausdorff space, and assume that its fundamental group is non-trivial. Does it always exist a simple curve in $X$ which is non-null-homotopic?

Such curve does exist if we further assume that $X$ possesses a universal cover.

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smyrlis
smyrlis
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Existence of a non-null-homotopic simple closed curve

Assume that $X$ is a path-wise connected Hausdorff space, and asuume that its fundamental group is non-trivial. Does it always exist a simple curve in $X$ which is non-null-homotopic?

Such curve does exist if we further assume that $X$ possesses a universal cover.