Talk:Spacetime topology

Stub

I've created this stub which, hopefully, will expand into a fairly comprehensive article. MP ^{(talk•contribs)} 20:47, 15 November 2007 (UTC)

Plural ?

I suggest renaming this article to “spacetime topologies”, because there is at least two (generally even three) topologies. Any objections? Incnis Mrsi (talk) 12:22, 22 December 2009 (UTC)

Actually, the current title is sufficient; otherwise we'd have to rename the Topology article 'Topologies' and Topological space to 'Topological spaces' and so on. I know this article is more specific, but the article explains the different topologies. :) MP ^{(talk•contribs)} 09:27, 24 December 2009 (UTC)

R4

I suppose that in this sentence:

As with any manifold, a spacetime possesses a natural manifold topology. Here the open sets are the image of open sets in $\mathbb {R} ^{n}$.

what is meant is: $\mathbb {R} ^{4}$.

Or am I missing something?

--David Olivier (talk) 09:14, 1 March 2011 (UTC)

Mathematically, the sets that are declared to be open in the manifold come with the definition of manifold, not as images of anything. Nevertheless, since charts to R4 (or Rn if one want to be general) are required to be continuous, the inverse image of open sets of R4 should be open sets of the manifold.Noix07 (talk) 13:25, 12 March 2015 (UTC)

How many topologies?

The article says "There are two main types of topology..." and then goes on to describe three. Is this a typo or have I misunderstood? -- Dr Greg  talk  15:43, 26 August 2012 (UTC)

There is even more confusion than this confusion. If I understand correctly, the interval topology ($I^{+}(x)\cap I^{-}(y)$) is the same as the path topology for any globally hyperbolic manifold (i.e. for any cosmology except pathological theories like Gödel metric). In a manifold with a closed time-like curve the interval topology will be coarser, likely even trivial. But the article actually mentions two topologies under the name "Alexandrov topology": the interval topology (Hausdorf) and the $I^{+}(x)$ topology (a coarser, non-Hausdorf). Apparently (an original research starts here), there is also a non-Hausdorf version of the path topology. Incnis Mrsi (talk) 19:11, 26 August 2012 (UTC)

I checked out the definition of interval topology, and the Alexandrov topology here seems not to be exactly the interval topology: here one defines open subsets whereas in the interval topology one defines closed subsets. I asked the question at http://math.stackexchange.com/questions/1182966/subbase-for-a-topology-defined-by-a-family-of-closed-sets Noix07 (talk) 13:29, 12 March 2015 (UTC)