Merging too close edit points of a curve

How to merge into a single point edit points of a curve that are too close to one another. For example, the curve has 4 couples of points the distance between which is less than 0.01. I’d like to merge all that points if they are under the tolerance. How is it feasible? I thought to employ the “Simplify Curve” component but apparently, it doesn’t work with a curve but with a linear curve. (14.6 KB)

Did you try Fit curve?

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Awesome! Great thank you! The component helped me. Do you know the logic of the component, what does it do?

I don’t know , maybe it is something like projection.
Check this with different methods (23.5 KB)

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Elegant solution as well