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fixed English/removed capitals
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YCor
YCor
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Existence of Topologically Transitive Maptopologically transitive map on Euclidean Spacespace

I was reading this post and wondered. Does there exist a topologically transitive (TT) map $f:\mathbb{R}^n\to\mathbb{R}^n$ when $n\geq 2$? I know that post asks for compactness and topological mixing(ness) but if we relax the requirement to only TT is it possible?

Note: If $\mathbb{R}^n$ is replaced by an infinite-dimensional Hilbert space, then the Ansari-Bernal theorem guarantees such a map much existexists; moreover it mustcan be linear... So maybe it can exist in the finite-dimensional case?

Existence of Topologically Transitive Map on Euclidean Space

I was reading this post and wondered. Does there exist a topologically transitive (TT) map $f:\mathbb{R}^n\to\mathbb{R}^n$ when $n\geq 2$? I know that post asks for compactness and topological mixing(ness) but if we relax the requirement to only TT is it possible?

Note: If $\mathbb{R}^n$ is replaced by an infinite-dimensional Hilbert space, then the Ansari-Bernal theorem guarantees such a map much exist moreover it must be linear... So maybe it can exist in the finite-dimensional case?

Existence of topologically transitive map on Euclidean space

I was reading this post and wondered. Does there exist a topologically transitive (TT) map $f:\mathbb{R}^n\to\mathbb{R}^n$ when $n\geq 2$? I know that post asks for compactness and topological mixing but if we relax the requirement to only TT is it possible?

Note: If $\mathbb{R}^n$ is replaced by an infinite-dimensional Hilbert space, then the Ansari-Bernal theorem guarantees such a map exists; moreover it can be linear... So maybe it can exist in the finite-dimensional case?

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ABIM
ABIM
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Existence of Topologically Transitive Map on Euclidean Space

I was reading this post and wondered. Does there exist a topologically transitive (TT) map $f:\mathbb{R}^n\to\mathbb{R}^n$ when $n\geq 2$? I know that post asks for compactness and topological mixing(ness) but if we relax the requirement to only TT is it possible?

Note: If $\mathbb{R}^n$ is replaced by an infinite-dimensional Hilbert space, then the Ansari-Bernal theorem guarantees such a map much exist moreover it must be linear... So maybe it can exist in the finite-dimensional case?