The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was Keep, article needs editing, not deleting. Tim Vickers (talk) 00:10, 24 June 2008 (UTC)[reply]

Tube lemma[edit]

Dear All,

I believe that this article should be either nominated for deletion or restarted (deleted and rewritten) for the following reasons:

1. The article does not provide a purpose or reason for proving the tube lemma.

2. The proof is correct but not appropriately structured.

3. A much simpler proof exists.

4. The article does not give the general form of the tube lemma which is a much stronger result than the tube lemma. This is another reason why the article should be restarted.

5. The article should properly define terminology such as what a slice is and what a tube is in dot points.

6. This is not the exact form of the tube lemma; the following is:

Let N be an open set containing {x} X Y for some x belonging to X where X and Y are topological spaces. If Y is compact, then there exists U open in X such that the tube U X Y contains {x} X Y and is contained in N.

Note the difference: N need not cover X X Y.

7. A proper proof should not require the use of projection maps. The result: If X is compact and Y is homeomorphic to X, then Y is compact, should be used in order to provide an easier proof. Basically, it should be stated clearly in the proof that the image of a compact space under a continuous map is compact.

8. The generalized tube lemma will give some purpose to this article; without it the article is not complete.

9. The article doesn't state that the purpose of the tube lemma is to prove that the product of finitely many compact spaces is compact and that the tube lemma cannot be generalized to arbitrary products.

10. The article doesn't supply any links to the Tychonoff theorem. It doesn't even hint at any relation between the tube lemma and compactness.

I hope you agree with all the reasons I have put forth. I am going to put up and AFD tag for the above reasons. Basically, my purpose is to remove this article and add a new article on the generalized tube lemma with applications to compactness. Since the article is short, this is a much better alternative than editing the article (which will be a much longer process).

Note that if this article is deleted, I wil start a new article on the generalized tube lemma which will be properly structured, and provide applications to compactness. Topology Expert (talk) 10:55, 23 June 2008 (UTC)[reply]

Keep. Articles do not need to be deleted in order to be improved. These are very good suggestions for improvement, but none of them suggest a compelling reason for deletion. siℓℓy rabbit (talk) 11:58, 23 June 2008 (UTC)[reply]
Keep per Silly Rabbit. Darrenhusted (talk) 12:54, 23 June 2008 (UTC)[reply]
Keep and make your suggested edits. _{TravellingCari}^{the Busy Bee} 13:23, 23 June 2008 (UTC)[reply]
Keep It has problems? WP:SOFIXIT! That's the whole point of a wiki. Calvin 1998 ^(t-c) 21:23, 23 June 2008 (UTC)[reply]
Note: This debate has been included in the list of Science-related deletion discussions. -- Fabrictramp | talk to me 00:02, 24 June 2008 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.