Talk:Metric space aimed at its subspace

From Wikipedia, the free encyclopedia

The material contained in this article describes research which is essential to other articles in wikipedia. They are category of metric spaces, injective metric space, tight span... Without this article the history of the topic would be distored and essentially incomplete. -- Wlod 02:48, 7 November 2007 (UTC)

Indeed, paper:

W.Holsztyński, On metric spaces aimed at their subspaces, Prace matematyczne, vol. 10, PWN, Warszawa, 1966, pp.95-100

was one of the early research, which considered the category of metric spaces with metric mapings as morphisms (the research which W.H. had started and got results from 1961 on). -- Wlod 07:53, 7 November 2007 (UTC)

[edit] anybody?

Is there someone knowledgeable about the wikipedia procedures who would resolve the unfortunate situation created by "Captain Panda"? -- Wlod 00:49, 8 November 2007 (UTC)

[edit] AfD?

The creation of this article by the writer of the only paper cited looks to be a violation of the Wikipedia:Conflict of interest guideline. If I did the search correctly, there are no citations found by MathSciNet to this paper at all. The creator of this article has authored a number of real math papers published in western journals, so to choose such an obscure topic for a new article seems likely to cause difficulty. Notability of this topic can't be established in the conventional way, due to lack of citations to the only reference, so I suggest that it be considered for deletion. EdJohnston 06:41, 11 November 2007 (UTC)

[EdJ moved User:Wlod's reply here. Wlod had originally responded at User_talk:EdJohnston]:

What wrong interest could I have in bringing my paper, published in an obscure journal, to the attention of some of the mathematical public? It looks that you did your research and recognized that I have publications in more recognized journals. Thus my reason is not to gain more recognition. I know what the authentic achievement means and I wouldn't care for a phony one. Thus what else? At the present time I remember only three stages of life: old, ancient and archeological. I am at the archeological stage. I am not competing for any academic or research or, say, AMS positions, or grants or whatever. At my stage, I am active mathematically simply because I like mathematics. OK, so much for the conflict of interests.

Thus why I have decided to write Metric space aimed at its subspace?   I gave part of the answer in the article and in its talk. Since the basic topic of injective (hyperconvex) metric spaces was presented at wikipedia, it's logical and nearly necessary to present also the Aim(X) functor. At wikipedia there is a tendency to iterate the edition of an article. I might consider a more complete functorial description of the topic.

Besides being an essential part and an illustration of the injective metric spaces theme, it also has a distinct elegance and geometric appeal. (Yes, I should do a better job presenting it).

There is a didactic reason for articles about the metric spaces, the category of metric spaces and metric maps, isometric embeddings, ...

On one hand it is an easy to grasp theory. On the other hand it is a very pleasing illustration of the workings of the theory of categories, e.g. the connection between the injective metric and Banach spaces. The theory of isometric embeddings, besides being attractive by itself, is just one step removed from the approximation theory. When you go in this direction then finally you get into deep, profound problems.

So, yes, the metric theory of metric spaces is mostly easy, while it is a healthy, juicy, geometry, which can be combined with the group theory (then you may run into hard mathematical problems) but it has a great didactic value for students, starting with high school, and for high school teachers too. In particular, the theory of metric spaces contains in a most natural way the graph theory, and, independently, some of the theorems on isometric embeddings have a strong graph-theoretic element in their background.

You may remove my article, but by doing so you will distort and cripple the presentation of metric spaces on wikipedia. It is ironic that for you the obscurity of the journal is the reason to remove the article from wikipedia. It should be the merit that counts. Thus it should be just the opposite to what you state: the obscurity of the original source is an extra urgent reason to have its valuable research presented and saved from obscurity by wikipedia.

(One more remark about Aim(X): it gives the most natural context for the classical Kuratowski-Wojdysławski isometric embedding).

Sorry for this long and chaotic comment. (It takes long to write a short one) -- Wlod 07:55, 11 November 2007 (UTC)