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Results tagged with at.algebraic-topology
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user 106622
Homotopy theory, homological algebra, algebraic treatments of manifolds.
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"Robust" Noninjectivity of a Continuous Mapping of a Sphere into the Plane
Let $X=\mathbb{S}^2$ and $Y=\mathbb{R}^2$ and $f:X\to Y$ a continuous mapping. Is it true that there must exist a nonempty set $V\subset f(X)$, open in $f(X)$ (in the subspace topology), such that eac …
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