User talk:OdedSchramm
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[edit] Circle packing theorem
Hello. I've just added Circle packing theorem to the list of circle topics. If you know of other articles that should be listed there and are not, could you add those or point them out to me? Thanks. Michael Hardy (talk) 18:05, 30 March 2008 (UTC)
[edit] Topology Expert
Dear Oded,
I feel that there is some misunderstanding. I am not a "hoax" (what do you mean by this?), and my intentions are good. I am not the type of person who likes to boast, and I would rather people didn't know that I was a professor. That is why I edited your post. I am sorry that I left your signature (I didn't know that I did this). I earlier claimed that I was a professor because I felt people were not believeing my mathematical claims. However, after creating a few articles, I believe that I will gain more respect. Also, I keep on getting messages regarding me being a professor so that is also why I edited your post. I hope you understand. Secondly, my intentions are good. I have recently created three articles:
All of these articles were either stubs or didn't have a page existent. I am also planning to do much more work on Wikipedia. Please see what I wrote on my talk regarding "supercompact spaces". I have also decided not to delete the article on supercompactness. Earlier, I wasn't familiar with Wikipedia and thought that only articles on major topics should be included. After seeing the page on "Supercompact spaces", I decided that I will also create pages on "minor"(though important!) topics and therefore created a page on linear continua. From now on I promise that I will be more understanding and not claim ownership of pages. I hope you understand me and that we will continue to collaborate in a friendly manner.
Topology Expert (talk) 01:25, 12 May 2008 (UTC)
Dear Topology expert: I am sorry that I called you a hoax. What I meant was that I thought that perhaps you are just trying to make fun of us. I can see now that your intentions are good and that you are doing good work. It is a bit hard to communicate with you. I am not sure if you are really reading what other editors have written to you. Finally, I see you no longer insist on including exercises in articles (we tried to explain this many times).
- Another point of style that is worth mentioning is that it is customary in wikipedia not to link every occurance of a technical term (such as open), but only the first one (or perhaps the first one in every section, in a long article). The idea is to link only if there is a good chance that the reader does not know the term.
- Also, when you state a theorem, or begin a proof, it makes sense to make them bold, so that they stand out. I.e. Theorem. Proof.
I hope that we can continue to communicate. Please let me know if you have read this. If I want to communicate with you - will you read what I write on your talk page? Oded (talk) 02:31, 12 May 2008 (UTC)
Dear Oded,
Thankyou for your response. I will definitely try to improve my article in terms of what you said. I was also wondering whether I could put my exercises some place else (if possible). I saw the wikibook on topology, and some things are incorrect. For example see the exercises in the section on local connectedness on Wikibook. I think that the Wikibooks could be improved in terms of exercises. Is it alright to put exercises there? Thanks for your help once again. Also, could you please write on my talk page next time? It is much easier for me to respond there.
Topology Expert (talk) 05:44, 12 May 2008 (UTC)
Dear Oded,
Thankyou for fixing up my article. I am not actually familiar with how to write mathematical symbols so I will have to learn. Also, the definition you gave for the deleted comb space is basically the same as mine, written in a different way. I noticed that you seem to be experienced in measure theory so perhaps you will know whether more pages are required on the subject. I don't know how much detail is necessary, but perhaps we could merge some related pages together. I think that the definition of an outer measure and the definition of the lebesgue measure fit together nicely so perhaps we could add a little bit about how the outer measure relates to the lebesgue measure? I am not so sure about this since I am not very familiar with Wikipedia. Could you please give me your opinion on this?
I also wanted to ask whether I could change the name of the article on 'locally connected spaces'. When I first created this article I thought that this concept has a connection with the concept of components of a topological space so I decided to add that in. I don't think there is a page written on 'components' anyway so maybe we could change the name of the article to 'Components and locally connected spaces' which is a much more appropriate name. Could you please tell me how to do this?
I also noticed that there is not much written on the concept of the uniform norm. They have only used this in the context of function spaces but perhaps the more general reader would also prefer a view relating to the product topology. I am happy to write a page on that if necessary. I was also thinking that (as you mentioned) pages on concepts such as 'mesacompactness' and 'orthocompactness' could be improved. They are indeed important in mathematics. I am looking to improve pages on more elementary concepts which do turn out to be important in other branches of mathematics.
Thankyou for your help once again.
Topology Expert (talk) 10:47, 13 May 2008 (UTC)
Dear Oded,
Sorry for the late response. I meant (when I said that I was going to add a page on the uniform topology), was that there are pages on how the uniform topology fits in the context of functions spaces, but there is no page relating to the uniform topology on RωSuperscript text. Some readers (particularly students), may prefer to read about the properties of the uniform topology on RωSuperscript text. Of course, I am not saying that we should delete the original pages, but maybe we can add a page on this. I am not so sure whether Wikipedia is a learning tool (i.e, information should be written with examples so that people can learn), so maybe we shouldn't add an extra page relating to the uniform topology on RωSuperscript text. But in my opinion, some people may want to also read how the uniform topology can be imposed on RωSuperscript text and some of its properties. Of course, the uniform topology is most used in functional analysis. Could you please give me your opinion on this?
Also, I recently added some information regarding the relevance of the 'induced homomorphism' in algebraic topology (about two pages on a word file). But, David Eppstein deleted what I wrote. Therefore, I asked him why he did this but perhaps you may know what was wrong with what I wrote (since you are familiar with Wikipedia). Thankyou for your help.
Topology Expert (talk) 08:47, 17 May 2008 (UTC)
Dear Oded,
I wasn't stating my intentions clearly; sorry for that. I really meant 'uniform metric' instead of 'uniform norm' so I did make a mistake. I (having learnt topology first from Munkres's text book), believe that perhaps we should include a new page on the uniform topology in relation to R^ω and other spaces (namely products of metric spaces). I feel opposed to my original intention in which I thought that beginners may find it beneficial to read a more elementary view of the uniform topology. Perhaps a functional analysis point of view may be a bit irrelevant for someone learning point-set topology. Now I see that Wikipedia is not for learning so perhaps it is not a good idea to include such a page. On the other hand, you mentioned earlier that Wikipedia is about putting maximum detail so I guess it is not such a bad idea. Could I please have your opinion on this? Thankyou for all your help.
Topology Expert (talk) 10:00, 19 May 2008 (UTC)
[edit] Uniform Topology
Dear Oded,
I wasn't able to respond to your previous message because of other committments. Sorry about that. I noticed that you removed the section on the local finiteness of topological spaces in the article 'locally finite collection'. I completely agree that it should be removed. But you wrote that the sentence, 'every locally finite space is finite' is false. According to the definition that was written under the section, this should be true. For example, the power set of an infinite topological space, is an example of a collection which is not locally finite (because it isn't point-finite). So basically, I was wondering why you wrote that the last sentence was false. I think that that section should be deleted anyway.
Also, the uniform topology does appear to have a name in textbooks. In the book by Munkres, it is referred to as the uniform topology and the metric that induces this topology is referred to as the uniform metric. As most people study the book by Munkres, it seems appropriate to title the article as 'uniform topology'. I was thinking of perhaps creating this article under this name. Perhaps you would know whether this should be done.
I also recently thought of some additional concepts that could be included in the article on 'Locally connected space'. Namely, the concept of a weakly locally connected space and the notion of quasicomponents. I feel that by adding this, I am including a bit too much information in this article. Maybe it would be better to split this article up. On a word file it takes up 7 pages which I don't think is appropriate for an article on this concept. On the other hand, there are many more things that can be added under this title and I am ready to add them. Could you please give me our opinion on this?
Thankyou for your help.
Topology Expert (talk) 08:00, 3 June 2008 (UTC)
The space Z (integers) is locally finite but infinite.
With regards to your other questions, I'll reply soon. --Oded (talk) 18:32, 3 June 2008 (UTC)
I don't not have a definite opinion as to whether we should have an article on the uniform topology, beyond the way it is currently covered. If all there is to say about the subject is what I know, then the answer would be no. Oded (talk) 05:12, 4 June 2008 (UTC)
Dear Oded,
I know this is a trivial matter, but according to the definitions I have seen (a space is locally finite if every collection of subsets of the space is locally finite), the integers shouldn't be locally finie. This is because the collection of all open subsets of the set of integers is not locally finite (because this collection isn't point finite). If you are correct, then the definition I have read is wrong. On the other hand, many reliable sources give the same definition as what I know. So I was just wondering how the definition you know is worded. Most probably, the definition I have got is wrong.
I thought about how the article on supercompacntess could be improved and I have some ideas. I was thinking of including some more spaces that are supercompact in the article. However, I am unsure whether I should do this. From what I have seen in mathematics articles, it is alright to include certain types of topological spaces that are supercompact. I am going ahead with this. If what I am doing is inappropriate for the article, could you please let me know?
Topology Expert (talk) 07:55, 4 June 2008 (UTC)
You are right about locally finiteness. I was a bit confused.
Regarding supercompactness: I think you initially wanted to delete the article, as you thought it was not important enough. Since I don't know much about supercompatness, I don't feel that I can give advice as to what to add to the article. Likewise, I would think that unless you have now become a supercompactness enthusiast and feel that you have a good idea of what are some of the important facts known (published) about supercompactness, that you should probably leave the possible expansion of the article to those who have the subject closer to their heart.
Oded (talk) 09:57, 4 June 2008 (UTC)
Dear Oded,
About local finiteness of a topological space, I believe that the following is a more appropriate defintion (in my opinion):
A topological space, X, is said to be locally finite, if every collection of disjoint subsets of X is locally finite.
The requirement that the sets be disjoint solves the problem and makes the statement, 'a space is locally finite iff it is finite' false. In this case, the claim that the integers is locally finite is true. However, most mathematics sources give a different definition. Truthfully speaking, the integers should be locally finite according to definition but isn't. In this definition it is. What is your opinion on this definition?
I happened to notice that there is no article on the broom space. I think that a definition of the broom space is worthwile in the context of weakly locally connected spaces (or possibly in other contexts) but I am not sure. Do you think that an article should be created on the broom space?
Thanks for your help.
Topology Expert (talk) 06:42, 8 June 2008 (UTC)
I don't think that there is any need to define a locally finite space. The first variant on the definition is just finite spaces, while the second variant is the same as being a discrete space (space with the discrete topology).
I don't know the broom space.
