Recent content by mr.tea

Sorry, fixed it.

Hi, I have a (probably stupid) question about the Baire Category Theorem. I am looking at the statement that says that in a complete metric space, the intersection of countable many dense open sets is dense in the metric space. Assume that we have the countable collection of dense open sets ##...

Thanks for the links. I am looking for a text which, as Gamelin and Green, tends more towards analysis and its application than just general topology. Thank you again.

I am taking a course in topology with Gamelin and Greene, Introduction to topology. I would like to have some supplement to extend and give more motivation and explanation. I am quite tired of the "theorem, proof, theorem, proof" pattern. Thank you!

By "layer of complication" I meant the definition of including an open set, at least for me, I feel that this is an unnecessary addition (if we define neighborhood to be open).

Yes. A set ##S## is a neighborhood of a point ##s\in X## if there is an open set ##U## containing ##s## and is contained in ##S## (##s\in U\subset S##). Being an open set is independent of being closed. A lot of the theorems are either want a closed or open sets, and neither open nor closed sets...

Thank you for the answer. So why do authors define it using inclusion of open set?

Hi,t I am studying topology at the moment. I have seen that some authors define the neighborhood of a point using inclusion of an open set, while others define the term as open set that contains the point. In most of the theory I have seen so far, the latter is more convenient to use. Why is...

We studied discrete math using Grimaldi's book (https://www.amazon.com/dp/0201726343/?tag=pfamazon01-20) and it was great. Contains also a lot of historical notes.

I am reading now "Computers Ltd.: What They Really Can't Do" by David Harel.

You can take a look at https://mathinsight.org/thread/multivar for explanation and http://tutorial.math.lamar.edu/Problems/CalcIII/DIGeneralRegion.aspx and https://faculty.math.illinois.edu/~hildebr/461/doubleintegrals-sol.pdf for practice problems, and every multivariable/vector/advanced...

Thank you for your answer! I am sorry. Can you explain a bit more about this part? Thank you very much, now it's understandable. Thank you.

I am trying to learn about free groups(as part of my Bachelor's thesis), and was assigned with Hungerford's Algebra book. Unfortunately, the book uses some aspects from category theory(which I have not learned). If someone has an access to the book and can help me, I would be grateful. First...

Hi, I am studying about circulant matrices, and I have seen that one of the properties of such matrices is the eigenvalues which some combinations of roots of unity. I am trying to understand why it is like that. In all the places I have searched they just show that it is true, but I would like...

I used the hardcover from our library(quite a lot I can say), both volumes, second edition, and I don't remember anything bad with the printing quality. They try to make it affordable, which is a good thing indeed. However, they should also keep the printing quality suitable for humans. Dover...