- #1
Tinyboss
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Here's an interesting question--I've asked some faculty members around here and "off the top of their head" none of them knows the answer. My gut says "yes", but my gut sucks at math. So here's the statement:
Suppose we have a function [itex]f:\mathbb{R}^2\to\mathbb{R}[/itex], with the property that for every line segment [itex]L\subset\mathbb{R}^2[/itex], the restriction [itex]f\big|_L[/itex] is continuous. Is [itex]f[/itex] necessarily continuous?
Suppose we have a function [itex]f:\mathbb{R}^2\to\mathbb{R}[/itex], with the property that for every line segment [itex]L\subset\mathbb{R}^2[/itex], the restriction [itex]f\big|_L[/itex] is continuous. Is [itex]f[/itex] necessarily continuous?