Posts Tagged 'metric spaces'

First Week of the Fall Term 2011 – Mathematics Graduate School

Gradient Flows by Luigi Ambrosio

It’s the second week of school, but with a bank holiday last Monday (09/12/11), graduate school started up slowly. It will take until next week until everyone is finally registered to all of their classes. It took me a while to do so as well, because they changed up the system from a program that you installed on your computer to an online version. The online version is better, but you need to know where to go. I finally registered to my classes last Tuesday. I have three this semester:

Topics in Geometric Analysis: This class is with my thesis advisor and we will be exploring gradient flows in metric spaces. We will be using Luigi Ambrosio’s book of the same title. It promises to be an interesting class. Although, it’s not exactly what I’d like to do in my thesis, it’s getting there. I’d like more measure theory, but luckily, my advisor is doing research in the field. There are six students in the class, but only 4 were registered on Monday. I don’t know if the other two will be registering, my guess is yes. Two of my classmates are the other graduate students of my advisor. We are all going to a workshop in Hsinchu in Differential Geometry  on Saturday. Since I work most Saturdays, it’s not really a problem getting up. It will be a break from the norm, and I have a keen interest in Differential Geometry.

Continue reading ‘First Week of the Fall Term 2011 – Mathematics Graduate School’

Compactification and Metrisation

Some great notes from Dr. Terence Tao’s lecture on compacity and metric spaces.

Metric spaces are sets with a measure of distance between each of its elements. Compact spaces are spaces in which each sequence (xn) admits a converging sub-sequence. This is called the Bolzano-Weierstrass property and such compact spaces are called sequencially compact. There is a more general way of defining a compact space, by saying that each of its open covers has a finite subcover.


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