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I initially asked this question on MSEMSE but I haven't had any luck.

The Whitney Approximation Theorem states that any continuous map between smooth manifolds is homotopic to a smooth map. If the manifolds are real analytic, is every continuous map between them homotopic to a real analytic map?

I know that the natural generalisation to complex manifolds fails. That is, not every continuous map between complex manifolds is homotopic to a holomorphic map.

I initially asked this question on MSE but I haven't had any luck.

The Whitney Approximation Theorem states that any continuous map between smooth manifolds is homotopic to a smooth map. If the manifolds are real analytic, is every continuous map between them homotopic to a real analytic map?

I know that the natural generalisation to complex manifolds fails. That is, not every continuous map between complex manifolds is homotopic to a holomorphic map.

I initially asked this question on MSE but I haven't had any luck.

The Whitney Approximation Theorem states that any continuous map between smooth manifolds is homotopic to a smooth map. If the manifolds are real analytic, is every continuous map between them homotopic to a real analytic map?

I know that the natural generalisation to complex manifolds fails. That is, not every continuous map between complex manifolds is homotopic to a holomorphic map.

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edit approved May 8, 2015 at 17:10
Ali Taghavi
edit approved May 8, 2015 at 17:10
Ali Taghavi
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Michael Albanese
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Is the analytic version of the Whitney Approximation Theorem true?

I initially asked this question on MSE but I haven't had any luck.

The Whitney Approximation Theorem states that any continuous map between smooth manifolds is homotopic to a smooth map. If the manifolds are real analytic, is every continuous map between them homotopic to a real analytic map?

I know that the natural generalisation to complex manifolds fails. That is, not every continuous map between complex manifolds is homotopic to a holomorphic map.