Can an Alternating Metric Define a New Spacetime Topology?

[Phrak]

Can an alternative topology of spacetime be defined upon a "mertic" of alternating forms?

A less stringent question: Can a topology be defined, without first premising a metric, but premising an alternating structure instead?

 

[Polyrhythmic]

What do you mean by "alternating forms/structure"?

 

[Mueiz]

Can an alternative topology of spacetime be defined upon a "mertic" of alternating forms?

A less stringent question: Can a topology be defined, without first premising a metric, but premising an alternating structure instead?

Yes ... but this new metric must be a function of the metric because the metric define the topology of spacetime completely.

 

[dslowik]

Yes ... but this new metric must be a function of the metric because the metric define the topology of spacetime completely.

What is the metric?

And, yes a metric will define a topology via it's open balls, the metric topology. But can we define another topology perhaps for other purposes? Can't the space be given another topology other than the metric topology?

 

[DrGreg]

Can an alternative topology of spacetime be defined upon a "mertic" of alternating forms?

A less stringent question: Can a topology be defined, without first premising a metric, but premising an alternating structure instead?

When you use the word "metric" do you mean in the topological-space sense or the metric tensor, which are two different concepts?

 

[dslowik]

That is a key point, Dr. Greg.
Where does that other metric come from, the one that defines the topology? The metric tenser is not a metric -not non-neg and no triangle inequality.
Also see my 'Flat spatime topology-metric?' thread in math -> topology and geometry sections

 

[Phrak]

When you use the word "metric" do you mean in the topological-space sense or the metric tensor, which are two different concepts?

I was thinking of the metric tensor. But now that you've brought it up, and I've had a chance to look at the Wiki page on the metric, I think the latter is what I want to know about. Thanks!