Talk:Spectral space

Omega

It is not clear what Omega is. Is it the topology of X? --MarSch 28 June 2005 16:52 (UTC)

There's no omega any more. 67.198.37.16 (talk) 17:41, 26 July 2016 (UTC)

Spectral theory

Could anybody explain the relationship (if a natural one exists) between spectral spaces and spectral theory? 128.62.97.227 19:13, 25 August 2005 (UTC)

There is none, in the ordinary, canonical sense. With a slight stretch of the definition of "related", see the section "Functional analysis perspective" of the article spectrum of a ring -- the eigenvectors are the "points" of the topology, from which you can then form ideals, and so on, and in fact, have a fair amount of overlap with operator theory. 67.198.37.16 (talk) 17:41, 26 July 2016 (UTC)

T₀ needed?

Any sober space is T₀, so there should be no need to require this latter condition. fudo (questions?) 13:06, 8 October 2008 (UTC)

Indeed. -- xmath (talk) 18:20, 5 March 2009 (UTC)

Some authors call a space sober if it is the closure of a point. To avoid confusion, the T₀ property should be stated explicitly. — Preceding unsigned comment added by Marcus0107 (talk • contribs) 23:20, 30 March 2017 (UTC)

Merge with coherent space

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

The result of this discussion was not merged D O N D E groovily Talk to me 03:55, 17 March 2012 (UTC)

---

There already is an article about Coherent spaces, which are the same thing. They should probably be merged. -- xmath (talk) 18:20, 5 March 2009 (UTC)

No. Spectral spaces have a completely different use than coherent spaces. —Preceding unsigned comment added by 67.194.132.91 (talk) 06:04, 17 April 2010 (UTC)

The pages should not be merged. Spectral spaces occur in a wide variety of areas in mathematics and are the standard terminology now. Coherent spaces are spectral spaces when viewed in a particular context of topology. (Marcus0107 (talk) 09:24, 12 March 2011 (UTC))

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.