Cotangent Bundle $T^{*}(M)=\bigcup_{m\in M} M_m^{*}$ (disjoint union of contangent space) Could any one explain me how there is a natural projection from $T^{*}(M)\rightarrow M$ given by $\pi(f)=m$ if $f\in M^{*}_m$? I am not able to understand and feel the map naturally Please explain.
construction of cotangent bundle
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differential-geometry