Английская Википедия:Boundary parallel

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Версия от 05:23, 11 февраля 2024; EducationBot (обсуждение | вклад) (Новая страница: «{{Английская Википедия/Панель перехода}} {{Unreferenced|date=December 2009}} In mathematics, a closed ''n''-manifold ''N'' embedded in an (''n'' + 1)-manifold ''M'' is '''boundary parallel''' (or '''∂-parallel''', or '''peripheral''') if there is an isotopy of ''N'' onto a boundary component of ''M''. ==An example== C...»)
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Шаблон:Unreferenced In mathematics, a closed n-manifold N embedded in an (n + 1)-manifold M is boundary parallel (or ∂-parallel, or peripheral) if there is an isotopy of N onto a boundary component of M.

An example

Consider the annulus <math>I \times S^1</math>. Let π denote the projection map

<math>\pi\colon I \times S^1 \rightarrow S^1,\quad (x, z) \mapsto z.</math>

If a circle S is embedded into the annulus so that π restricted to S is a bijection, then S is boundary parallel. (The converse is not true.)

If, on the other hand, a circle S is embedded into the annulus so that π restricted to S is not surjective, then S is not boundary parallel. (Again, the converse is not true.)