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J. GE
J. GE
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Is Level set of Regular functions in Alexandrov spaces again an Alex. space?

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J. GE
J. GE
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Let $X^n$ be an Alexandrov space, and $f: X^n\to \mathbb R^n$$f: X^n\to \mathbb R^k$ a regular map, does the level set necessary be an Alexandrov space?

In my mind, the intrinsic metric on the level set is 'comparable' to the ambient metric., but is it necessary an Alexandrov space?

Let $X^n$ be an Alexandrov space, and $f: X^n\to \mathbb R^n$ a regular map, does the level set necessary be an Alexandrov space?

In my mind, the intrinsic metric on the level set is 'comparable' to the ambient metric.

Let $X^n$ be an Alexandrov space, and $f: X^n\to \mathbb R^k$ a regular map, does the level set necessary be an Alexandrov space?

In my mind, the intrinsic metric on the level set is 'comparable' to the ambient metric, but is it necessary an Alexandrov space?

Source Link
J. GE
J. GE
  • 1.1k
  • 1
  • 9
  • 15

Level set of Regular functions in Alexandrov spaces

Let $X^n$ be an Alexandrov space, and $f: X^n\to \mathbb R^n$ a regular map, does the level set necessary be an Alexandrov space?

In my mind, the intrinsic metric on the level set is 'comparable' to the ambient metric.