7:06 AM
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Do we really need basis? More specifically, there are different notions of basis in mathematics, and the tag is practically useless without adding a distinction between them.

It might be a useful tag. In any case: a) If we decide we do not want the tag, it should probably be made synonym of (linear-algebra). (As to prevent repeated creation of the same tag.) b) If we decide that we want this tag, then the tag-wiki should definitely be clarified. (For example, there are some questions about basis for a topology in this tag at the moment.) Link to a related conversation in chat: chat.stackexchange.com/rooms/3740/conversation/basis-tagMartin Sleziak Jun 30 at 17:31
Martin, at 30 questions and gaining, this tag becomes a big mess. Any advice? — Asaf Karagila 8 hours ago
I created tag-info which says that this is for questions for basis of a vector space. I will try to retag the questions which do not belong here and add (linear-algebra) to questions which do not have this tag. (This activity might help some other users to notice the issue.) If you prefer to get rid of this tag, you can either suggest a synonym (basis) -> (linear-algebra) and wait for enough users to vote. Or you can open a separate thread on meta, if you prefer. — Martin Sleziak 37 secs ago
Questions which do not belong into this tag, if we want only keep it for questions from linear algebra:
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I want to prove that the Order topology on $\mathbb{R}$ has the same basis as as the Euclidean topology on $\mathbb{R}$. Assume that the only thing we know about the order topology is that it has the open rays as its subbase. My problem is that at some point I have to make some kind of claim tha...

1

Consider our manifold to be $\mathbb{R}^n$ with the Euclidean metric. In several texts that I've been reading, $\{\partial/\partial x_i\}$ evaluated at $p\in U \subset \mathbb{R}^n$ is given as the basis set for the tangent space at p so that any $v\in T_pM$ can be written is terms of them. The ...

0

Using basic open sets of $\Bbb R$, prove that $f(x,y,z)=x^2+y^2+z^2+2x+2y+6$ is a continuous function from $\Bbb R^3$ to $\Bbb R$. My attempt: Since $f(x,y,z)$ is continuous and $f(x,y,z)\in \mathcal B$ , where $\mathcal B$ is the basis of $\Bbb R$, (I.e. the collection of all open intervals $... 1 Show that the collection of all open intervals$\{(a,b)\}$is a basis of$\Bbb R$with the standard topology: My attempt: I believe we want to show two things: 1) All elements,$x\in\Bbb R$are contained in some basis element:$\forall x\in\Bbb Rx\in(x-1,x+1)\square$2) If$x\in B_1\...

Maybe this?
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In the paper 'Self-taught learning: transfer learning from unlabeled data' by Raina et al, the authors define a term as follows: 'aj(i) is the activation of basis bj for input xu(i) I have not encountered the term 'activation of a basis' before, and have been unable to find a definition of ...

### (basis) tag

Jun 23 at 10:49, 19 hours 1 minute total – 16 messages, 1 user, 0 stars

Bookmarked Jun 30 at 17:29 by Martin Sleziak

7:22 AM
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The basis was recently created. But it's a horrible tag. There are different notions of basis in mathematics, and they are not entirely the same at all. Hamel basis Hilbert basis. Schauder basis. Topological basis. The tag is used as a free for all. I believe it should be deleted or blacklis...

8:19 AM
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We know that there are $3$ types of $\mathcal{S}$-type Spaces, namely $\mathcal{S}_\alpha\:,\: \mathcal{S}^\beta\:,\:\mathcal{S}_\alpha^\beta$. $\mathcal{S}_\alpha: |x^k\varphi^{(q)}(x)|\le C_qA^kk^{k\alpha}\qquad (k,q=0,1,2,...)$ \$\mathcal{S}^\beta: |x^k\varphi^{(q)}(x)|\le C_kB^qq^{q\beta}\q...

I see you created new tag called (gelfand-shilov). Is it intended for Gelfand-Shilov spaces? As a tag creator, could you perhaps take some time to explain the intended usage in the tag-info? — Martin Sleziak 33 secs ago
BTW does anybody have an idea what is for.
There are two questions in that tag. The above and:
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Is there any expression for the integral of the product of three Meijer-G-functions, where the domain of integration is [0;1]?

2 hours later…
10:38 AM
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I see a lot of questions like: What is the next term in the sequence 20,5,3,6,7,12, ... ? I think they are asked daily. They are generally closed, but can't we do anything to reduce the number of questions asked in this manner? Furthermore, I think it would be good to point out that the qu...