Let-M-be-a-compact-smooth-manifold-of-dimension-d-Prove-that-there-exists-some-n-Z-such-that-M-can-be-regularly-embedded-in-the-Euclidean-space-R-n-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 165756 by CrispyXYZ last updated on 07/Feb/22

Let M be a compact smooth manifold of dimension d. Prove that there exists some n ∈Z^+ such that M can be regularly embedded in the Euclidean space R^n .

$$\mathrm{Let}\:{M}\:\mathrm{be}\:\mathrm{a}\:\mathrm{compact}\:\mathrm{smooth}\:\mathrm{manifold}\:\mathrm{of}\:\mathrm{dimension}\:{d}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exists}\:\mathrm{some}\:{n}\:\in\mathbb{Z}^{+} \:\mathrm{such}\:\mathrm{that}\:{M}\:\mathrm{can}\:\mathrm{be}\:\mathrm{regularly}\:\mathrm{embedded}\:\mathrm{in}\:\mathrm{the}\:\mathrm{Euclidean}\:\mathrm{space}\:\mathbb{R}^{{n}} . \\ $$

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Let-M-be-a-compact-smooth-manifold-of-dimension-d-Prove-that-there-exists-some-n-Z-such-that-M-can-be-regularly-embedded-in-the-Euclidean-space-R-n-

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