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What is Understanding Smooth Maps in Manifolds about?

This document summarizes key concepts about smooth maps between manifolds: - A map between manifolds is smooth if its coordinate representations are smooth functions. - Examples of smooth maps include inclusion maps, quotient maps, and projections. - Partitions of unity allow smoothly gluing together smooth maps to create new smooth maps. Cutoff functions and bump functions are used to construct partitions of unity. - Manifolds admit partitions of unity because they are paracompact, meaning every open cove

Author

Henry Rojas

Language

EN