Monsieur Ejemplé

Give an example of a function f:R^2 --> R s.t. the function is not continuous at zero, but for any (straight) line L passing through the origin, the induced function f|L is continuous on L.

OP
>>11
I wasn't thinking straight when I said your first one was correct.  Either way, my one in >>5 is pretty good.

>>10
You're right. The idea of an induced function is basically what it looks like.