Real Analysis Algorithms

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first posting here!

I would like to know if anyone knows a website, blog, book or repository that contains some basic principles of Real Analysis written in an algorithmic way.

I am learning some principles of topology, to then study continuity, limits and derivatives.

Making algorithms for sequences and series helped me a lot to understand the principles involved in these subjects, but it has not been easy to think about algorithms in topology...

This sample book was the closest I found:

https://books.google.com.br/books?id=K0B8BwAAQBAJ&lpg=PP1&hl=pt-BR&pg=PP1#v=onepage&q=cauchy&f=false

Thank you so much guys!