It is usual to have tensors in general relativity with discret index in the integer numbers. I propose to have index in the real numbers so that we can have for example:

$$\tilde A^t =\int_{-\infty}^{+\infty} A^{t'} (\frac{\partial \tilde x^t}{\partial x^{t'}}) dt'$$

The differential of a function is:

$$df=\int_{-\infty}^{+\infty} \frac{\partial f}{\partial x^t} dx^t dt $$

We have also:

$$\int_{-\infty}^{+\infty}(\frac{\partial \tilde x^t}{\partial x^{t'}})(\frac{\partial x^{t'}}{\partial \tilde x^{t''}})dt'=\delta (t-t'')$$

The sums are replaced by integrals. The points of the manifold are replaced by smooth functions. The coordinates are:

$$x^t(f)=f(t)$$

Can we make Einstein general relativity with continuous tensor calculus?