Prep for Hawking/Ellis: Point Set Topology Needed

In summary, the person is trying to prepare to read a book on the large scale structure of space-time but is struggling with the required knowledge of point set topology. They are asking for a short list of topics from point set topology that they need to learn before understanding the book. The speaker suggests continuing to read the general topology textbook and using additional references as needed, rather than getting bogged down in preparation.
  • #1
Andrew Kim
12
6
I'm trying to prepare to read The Large Scale Structure Of Space-time by Hawking and Ellis. I've been reading a General Topology textbook since the authors say "While we expect that most of our readers will have some acquaintance with General Relativity, we have endeavored to write this book so that it is self contained apart from requiring a knowledge of simple calculus, algebra, and point set topology." Can somebody who has read the book create a short list of topics from point set topology that I need to learn before understanding the content? I could simply continue reading the rest of the General Topology textbook (Bourbaki) but it's a bit mind numbing and confusing at the same time, and I suspect much of the topics that I would read about are not necessary for a book about GR.
 
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  • #2
I think the answer to this (and similar questions like it) relies on what specifically are you hoping to get out of the book. Are you looking to prove everything rigorously? Or just get some overview of methods and methods of calculation? Or something in between?

For me, I would just march onward. If I get stuck on something I really want to know but I am not adequately prepared for it, then I use another reference alongside it. Otherwise, I fear that I will get bogged down on getting prepared/overprepared rather than getting to what I really want.

My $0.03.
 
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1. What is point set topology?

Point set topology is a branch of mathematics that studies the properties of points, sets, and their relationships in topological spaces. It is used to describe and analyze the structure of a space without relying on measurements or coordinates.

2. Why is point set topology important?

Point set topology is important because it provides a framework for understanding and analyzing complex mathematical structures, such as manifolds and topological spaces. It is also used in various fields of science, including physics, computer science, and engineering.

3. What are the basic concepts in point set topology?

Some of the basic concepts in point set topology include open and closed sets, continuity, compactness, and connectedness. These concepts help define the properties of a space and how its points are related to each other.

4. How is point set topology related to general relativity?

Point set topology is used in general relativity to study the topology of spacetime. It helps describe the curvature and structure of the universe, as well as the behavior of particles and objects moving through it.

5. What are some real-world applications of point set topology?

Point set topology has various real-world applications, including image and signal processing, data analysis and clustering, and network analysis. It is also used in computer graphics and animation, as well as in modeling and simulating physical systems.

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