- #1

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- TL;DR Summary
- I am trying to prove the statement i will print below, there is not much to talk here.

I am not sure how to start it, but yet, i imagined it:

Be ##\phi^{X}, \phi^{Y}## two charts from an open set ##A, B## to ##R^{n}##:

##\phi^{X}: A -> R^{n}##, where ##\phi^{X}## is continuous

##\phi^{Y}: B -> R^{n}##, where ##\phi^{Y}## is continuous

##\phi^{X}: A -> R^{n}##, where ##\phi^{X}## is continuous

##\phi^{Y}: B -> R^{n}##, where ##\phi^{Y}## is continuous

I believe we need to show that ##\phi^{X}+\phi^{Y}: U = A\bigcup B -> R^{n}##, where ##\phi^{Y} + \phi^{X}## is continuous. But i am not sure how.