Tagging

5:10 AM

re propoduct-spaces: my concern is somewhat different. A question "For fin dim vector spaces, show that dim V x W is dim V + dim W" is also a question about product spaces. I do not think the tag should be used. The wiki allows it though. Maybe the "for example" should be changed, and tag be actually restricted to top and measure theory (conceived broadly).

I am looking at questions which have this tag and are not from topology or measure theory. It seems reasonable to look for them among questions without general-topology or measure-theory tag.

There might be a few questions among those search results which would probably deserve adding general-topology tag.

There are some questions which are either mistagged or use the tag product-space instead of (currently non-existent) cartesian-product.

is a set isomorphic to the product space of it's partition?

Better way to represent $f: I \to \cup_i T_i$, s.t. $ f(i) \in T_i, \forall i \in I ? $

Products containing the same digits

There are questions about various products of normed spaces. Would we want such questions in product-space tag?

Prove statements about complement in $\mathbb C$-Banach Space

Norms on an Ultraproduct

There are some questions about products of metric spaces.

Functional Analysis: countable Product of Compact Subsets of Metric Spaces is compact

Prove that d is a continuous real valued function on $M \times M$

Uncountable product in the category of metric spaces.

There are questions about products of manifolds.

Product of Riemannian manifolds and volume element

Second derivative/tangential map on a product manifold

I am not entirely sure, but I guess this one use (product-topology) tag simply in place of (cartesian-product).

Probability of Union of Events in a Probability Product Space By Counting Event Size

And I was about to add (general-topology) to this question:

Is a subspace of a product space also a product space?

But I see in the revision history that it was removed and there is also this comment:

Note that your question is not really related to the topology. Your $W$ is definitely a counterexample, no matter what the topology is. — John Ma Nov 14 '15 at 4:40

I am aware that there might be many other questions which are far from topology and measure theory in product-space tag. Looking at the above questions - i.e., the questions which have product-space tag but neither general-topology nor measure-theory - was just to get a rough idea what other questions are currently using this tag.

Again, I did not check all questions in product-space tag, but since there are no questions tagged either product-space+linear-algebra or product-space+vector-spaces, it seem likely that currently there are not that many questions about products of vector spaces in that tag.

@quid If we decide to clarify usage of product-space tag, we should decide, for example, whether product of normed spaces or products of metric spaces belong there. (It might be bit of a stretch, but basically they can be still considered product topology.)

But that is probably discussion for later. It might be worth separate meta question.

That optimization vs. maxima stuff is more important - it will affect more questions if it is changed. But since we discussed product-spaces and product-topology in the comment here, I thought it was worth having at least a cursory look at the questions in that tag and what other areas they come from.

Transcript for

$Mathematics$ Tagging