**UM Math Graduate Student Seminar**

Hao Kang

* University of Miami *

**will present**

**On Some Classical Analysis Problems by Baire Category Theorems**

Friday, February 10, 2017, 5:00pm

Ungar Building Room 402

**Abstract: **

In this talk, I will review Baire Category Theorem (BCT) and see some classical analysis problems in the view of functional analysis, including:

1. Is there a function of C[0,1] continuous at rational points but discontinuous at irrational points?

2. How "many" functions continuous everywhere but differentiable nowhere?

3. Do the Fourier series of every continuous periodic function converge to itself point-wise?

Some derived theorems from BCT such as uniform boundedness theorem and open mapping theorem and in particular their applications are also introduced.

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