User talk:Plclark

Welcome!

Hello, Plclark, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

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I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or place {{helpme}} on your talk page and ask your question there. Again, welcome!  Theresa Knott | Taste the Korn 22:37, 27 January 2007 (UTC)

Style note

Hi. Just a note regarding this diff. One should not hit the "Enter" key when writing text, as that breaks the line of text and is hard to see in the diff (look at the last part of the green text in two columns for what I mean).

Also, using an edit summary helps. Cheers, Oleg Alexandrov (talk) 15:04, 13 August 2007 (UTC)

Number theory AfD nomination

I have reverted your AfD tag on number theory which is in Wikipedia:Vital articles and is the main article in Category:Number theory with over 1000 articles including subcategories. If you really want to go through with this absurd nomination then you must create an AfD page with your reason as described in Wikipedia:Articles for deletion#How to list pages for deletion. The article content may be imperfect but there is no chance an article on such an extremely notable subject with a huge number of books and other reliable sources will be deleted, so a nomination would be a waste of time. PrimeHunter 03:11, 28 August 2007 (UTC)

Manual of Style

I just read your user page and thought you might find Wikipedia:Manual_of_Style useful. Hope it helps! -Rushyo (talk) 01:20, 6 July 2008 (UTC)

Separable space

Can you respond to http://en.wikipedia.org/wiki/Talk:Separable_space#Mistake.3F please? Thank you. —Preceding unsigned comment added by 77.4.188.4 (talk) 17:45, 7 July 2008 (UTC)

One-point compactification

Dear Plclark,

I don't think that I make many mistakes although I do sometimes (everyone makes a mistake once in a while). Therefore, I would like to ask you to specifically point out any mistakes that I have made (it is not that I am denying the fact that I have made mistakes but I want to know where exactly). When I contribute to articles, I normally 'write my knowledge' on those articles (except for my own research). If I have made a mistake, it is probably due to the following reasons:

• I was in a bit of a hurry

• I got the fact from a reference but I didn't read that fact carefully enough and therefore wrote something else (i.e, I was mindlessely editing Wikipedia)

• Of course, there is also the possibility that I simply did make a mistake

Sometimes I spare myself 10 minutes to edit Wikipedia and write something. If I spend more than one hour editing Wikipedia, I am probably creating a new article. The mistake I made about the one-point compactification was a bit silly; I intended to write that if X is homeomorphic to Y, then the one-point compactification of X is homeomorphic to the one-point compactification of Y. After your post about my mistake, I opened a book and saw an exercise asking one to prove that one-point compactifications are characterized up to homeomorphisms. This statement led me to believe that I was correct. However, using my knowledge I realised the mistake. From now onwards, I will edit Wikipedia during long periods of time in-order-to avoid such mistakes.

Note also, that I have experience in mathematics and making mistakes is not my nature. So generally, most of my mistakes are not caused because my understanding of the concept is poor. I in general edit articles on concepts that I know very well. I research mostly all branches of mathematics related to topology.

Thanks

Topology Expert (talk) 08:15, 13 July 2008 (UTC)

Note: Have you read my comment regarding separable spaces on Oded's talk page? I think that example is probably the easiest to understand (you do not need to go into complications).

I do not know of any mathematical mistakes in your edits that have not already been pointed out by me (just the one about one-point compactifications) or Oded, all of which you have already acknowledged and fixed, so far as I know. Revisiting issues which have already been resolved does not seem productive.

The one consistent mistake that I see, and that concerns me, is a wikipedic mistake rather than a mathematical one: you do not seem to have yet realized that your work must conform to the standards of verifiability. Several of your articles lack references entirely, and I do not think that any of the articles you have created have inline citations. Other people have asked you about this and you have responded by saying things like "How can I reference a definition?" or "There is no room for improvement here" that make me think you're not getting the point. In fact the former is a serious issue: if you're not extremely careful that your definitions are consistent with the literature and with the rest of wikipedia, the whole enterprise comes crashing down. In the case of the article on perfect spaces, I think you have the wrong definition: your article does not concern perfect spaces as they appear in the topological literature but rather perfect subsets of (usually metrizable) spaces. How could we possibly resolve this issue without citations to the literature?

I hope that before you start any new articles you will spend some time adding references for some of the articles you have already edited. Plclark (talk) 10:14, 13 July 2008 (UTC)Plclark

I'm not sure exactly what you're referring to about separable spaces, but it was not I who asked anything about them. Plclark (talk) 10:14, 13 July 2008 (UTC)Plclark

Every compact space is sequentially compact; this is an obvious fact in topology and I am surprised that you do not know about it. Also, you said that a sequence is a function from the natural numbers to the space in question (call it X). Consider the sequence {1/n}_{n is a natural number}. The sequence is the range of a particular function and not the function itself. Some texts refer to a sequence as a function from the natural numbers whereas other texts refer to a sequence as the range of a function from the natural numbers. I think that since Wikipedia refers to a sequence as you do, I should have followed the same convention.

However, I still would like you to give me the exact counterexample (not referring to an article) of a compact space that is not sequentially compact. I think that any textbook in topology will tell you that every compact space is sequentially compact. In fact the article on sequentially compact space does have a reference to Munkres' book and you will find that according to Munkres' every compact space is sequentially compact.

From you writing, it seems that you have the same attitude as Oded. If I make one mistake, everything I write should be considered a mistake. If I review everything you edit, I am more than likely to find some mistakes.

Topology Expert (talk) 03:08, 14 July 2008 (UTC)

As I said, the article compact space contains the example $\{0,1\}^{c}$ with the product topology as an example of a compact space which is not sequentially compact. Previously it was unsourced, but I added a citation to an article of Scarborough and Stone which gives this example (with proof). On p. 209 of Ryszard Engelking's General Topology, he gives the Stone-Cech compactification of the natural numbers as another example, with proof.

Your response to this issue is a good example of what I am talking about. You have claimed that compact implies sequentially compact is "obvious", but you have given neither any argument for it nor any clear citation. You also say "according to Munkres' every compact space is sequentially compact" but you don't say where in Munkres' book this appears. Thus in order to do verify (or, much more likely in this case, verify that it is not the case) this assertion I would have to read Munkres' book from cover to cover. Previously you had claimed that Munkres defined a nowhere dense set as one with empty interior: again this is almost certainly not the case, but it would be very time consuming for someone else to check this.

I have thus far assumed good faith in all my dealings with you. However, your repeated insistence that standard references say things that they do not say in order to defend yourself is beginning to make me question that assumption.

Finally, of course I will be grateful for any mistakes you may find in my edits.

Plclark (talk) 04:27, 14 July 2008 (UTC)Plclark

Your 'counterexample'

Dear Plclark,

Actually, I did make a mistake (again). Compactness implies sequential compactness for first countable spaces. However, you also made a mistake by saying that {0,1}^c is compact but not sequentially compact. The space is sequentially compact if c is a countable index set (since in this case the space is first countable) but not sequentially compact otherwise. I hope that this gives evidence of the statement that everyone makes mistakes.

Thanks

Topology Expert (talk) 10:54, 14 July 2008 (UTC)

By c I meant "continuum". Recall that I had referred you to this counterexample earlier; the full statement appears, with reference, in the article on compact spaces.

Again, I assumed good faith on your part even though records show that others have had issues with this in the past. Equivocating to try to demonstrate that I made a mistake (which in any case was not on an article) is not helping: surely you are not suggesting that if I can also make mistakes (which, of course, I can) then that excuses you from writing articles which are verifiable and correct?

I will ask you to fix these mistakes on sequentially compact space and to specifically retract your claims that Munkres says that nowhere dense subsets are by definition those with empty interior and that all compact spaces are sequentially compact. Otherwise there is no point in further discussion. Plclark (talk) 11:25, 14 July 2008 (UTC)Plclark

Discussion on Perfect space

Dear Plclark,

According to Rudin's 'Principles of mathematical analysis' (third edition), page 32, definition 2.18 (h), a subset E of a metric space X is perfect if E is closed and if every point of E is a limit point of E (i.e E has no isolated points). Note that in a metric space, every closed set is a G_δ set. In particular this implies that the definition you found is not equivalent to Rudin's definition for metric spaces (Rudin requires the additional condition that the metric space has no isolated points; according to your definition every metric space is perfect). However, the definition in Rudin's does imply yours, i.e Rudin's definition is stronger that yours for metric spaces. I just had a glimpse at chapter 2 of Rudin's book and I noticed that many of his proofs about compactness in metric spaces inexplicitly use the fact that metric spaces are Hausdorff (for instance theroem 2.34, page 37). In fact most of his theorems about compactness do generalize to arbitrary Hausdorff topological spaces. Therefore, I am led to believe that despite the fact that Rudin only considers metric spaces in the definition of perfectness, his definition probably does apply to arbitrary topological spaces.

Note also that I was not the one to give the definition of a perfect space; I expanded upon the definition. The creator of the article defined a perfect space as a topological space that has no isolated points. I think that it is best to question the creator as to why he defined perfect spaces in this way. Most probably, he referred to Rudin's book when giving the definition.

Topology Expert (talk) 11:11, 17 July 2008 (UTC)

RFC regarding Fowler&fowler

Hi Plclark. Thanks for your contributions in the discussion on Atiyah. I noted, that although WP:BLP was quoted several times in the debate, no attempt was made to apply it to C.K. Raju and other living individuals. I felt that you corrected User:Fowler&fowler on this point a few times; so did others, but he continued making -- what in my opinion -- are personal attacks on Raju. I have created a RFC requesting that he be asked to delete these comments and be restrained from making future such libelous edits. I feel that you were one of the editors who tried to resolve this dispute on the talk page and so, if you feel, my summary is accurate please certify it. thanks, Perusnarpk (talk) 21:53, 28 July 2008 (UTC)