If f :S2 → ℝ2 is C1 then f-1 (y) is finite for “most“ points y ∈ ℝ.
Two lines in ℝ3 do not intersect “in general.“
If f: ℝ→ ℝ is C1, “almost all“ horizontal lines in ℝ × ℝ are nowhere tangent to the graph of f.
“Generically“ a C1 immersion S1 → ℝ2 has only a finite number of crossing points.
KeywordsMeasure Zero Strong Topology Differential Topology Submanifold Complex Residual Subset
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