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- #1

- Feb 29, 2012

- 342

Thanks for all.

- Thread starter Fantini
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- #1

- Feb 29, 2012

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Thanks for all.

Metric space topology I would say is just real analysis.

Thanks for all.

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- #3

- Feb 29, 2012

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In that case what would you recommend for a self-study?

Rudin or Royden.In that case what would you recommend for a self-study?

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- #5

- Feb 29, 2012

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By Rudin you mean the "Big" one, "Real and Complex Analysis"?

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- #6

- Jan 26, 2012

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As for topology, have you considered Crossley's

Note: Baby Rudin = Principles, Papa Rudin = Real and Complex. Grandpapa Rudin = Functional, I suppose.

If you have the knowledge for it, yes. If not, start little and then go big.By Rudin you mean the "Big" one, "Real and Complex Analysis"?

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- #8

- Feb 29, 2012

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I'm done with all calculus 1-3 (single, multivariable and differential equations); done linear algebra and advanced linear algebra (PhD level); did Analysis I about a year ago but it was horrible, I learned almost nothing. The teacher focus' was more on calculus than proofs and intuition, which resulted in a pass without the appropriate maturity and knowledge developed.

As of now, I'm starting Analysis II, Analysis in \( \mathbb{R}^n \) (or on Manifolds) and Groups and Representations. As for books used, in the bibliography for the first there's "Methods of Real Analysis" by Goldberg, the teacher in \( \mathbb{R}^n \) is using "Calculus on Manifolds" by Spivak, but has said he'll use at times "A Comprehensive Introduction to Differential Geometry, volume 1" for a few things (I've also decided on taking Munkres' "Analysis on Manifolds" as a reference, studied differentiation using it before classes began and I enjoyed it), last but not least there were no recommendations for Groups, it was said that any book containing the basic ideas of groups would suffice, and I chose Rotman's "Introduction to the Theory of Groups" as my guide.

The idea of studying topology/metric spaces would be in parallel with those three.

- Jan 26, 2012

- 37

Chapter 1 : Set Theory (Axiom of Choice / Zorn's Lemma, Cantor-Bernstein , Countability, etc.)

Chapter 2 : Metric Spaces

Chapter 3 : Topological Spaces

Chapter 4 : Systems of continuous functions ( Urysohn's Lemma, etc. )

Chapter 5 : Basic Algebraic Topology

And all of this in roughly 200 pages, plus beautiful exposition!

All I can say, I remember well what general topology means. However, I also remember when topology was mixed with Banach spaces and Hausdorff spaces, just to approach Weirstrass calculus from general and more particular point of views. It was as obscure as it sounds, but it was correct, so I cannot object. I remember it was mixed, but I do not want to remember anything about it. (I still have nightmares about the exam. )

I vote for "General topology" if you like an abstract approach. More abstract, less details, more clear and easy.

I vote for "General topology" if you like an abstract approach. More abstract, less details, more clear and easy.

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- #11

- Feb 29, 2012

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