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2 votes
0 answers
128 views

Making a continuous function into embedding by adding additional dimension

While doing my researches, I encountered the following problem. Let $f:[0,1]^n\rightarrow \mathbb{R}^{n+k}$ be an arbitrary continuous function. I want to make this function an embedding by perturbing ...
6 votes
1 answer
181 views

Can we approximate a vector field on the plane with non-vanishing vector fields in $W^{1,2}$?

Let $V$ be a compactly-supported vector field on $\mathbb{R}^2$, whose zeros inside some open neighbourhood of the closed unit disk $\mathbb{D}^2$ are isolated. Does there exist a sequence of ...