# Bases for Tangent Soaces and Subsaces ... McInerney Theorem 3.3.14 ... ...

#### Peter

##### Well-known member
MHB Site Helper
I am reading Andrew McInerney's book: First Steps in Differential Geometry: Riemannian, Contact, Symplectic ... and I am focused on Chapter 3: Advanced Calculus ... and in particular on Section 3.3: Geometric Sets and Subspaces of [FONT=MathJax_Math]T[/FONT][FONT=MathJax_Math]p[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_AMS]R[/FONT][FONT=MathJax_Math]n[/FONT][FONT=MathJax_Main])[/FONT] ... ...

I need help with an aspect of the proof of Theorem 3.3.14 ... ...

Can someone please explain/demonstrate explicitly why $$\displaystyle (e_1)_p, (e_2)_p, \ ... \ ... \ , (e_{n-1} )_p$$ are the standard basis vectors for $$\displaystyle T_p( S_f )$$ ...

Help will be much appreciated ... ...

Peter

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The above post mentions Theorem 3.3.13 so I am providing text of the theorem together with a relevant definition ... as follows: