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
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))