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bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 25
visits member for 2 years, 8 months
seen 12 hours ago

Postgraduate student at the University of Bath, UK, studying geometry and representation theory. Currently thinking about cluster algebras and related objects.


Aug
19
comment Injection, Surjection, Bijection (Have I done enough?)
I guess in light of your comments on 3, I should clarify mine. While it is true that using continuity together with knowledge of the limits at each infinity provides a proof of surjectivity, it looks from the original question like the OP is trying to claim that continuous functions are necessarily surjective, hence my objections.
Aug
19
comment Injection, Surjection, Bijection (Have I done enough?)
Your definition is now correct. Any function to $\mathbb{R}$ with range $\mathbb{R}$ is surjective - but the same formula defines a function $\mathbb{R}\to\mathbb{C}$ which still has range $\mathbb{R}$ so is not surjective. In general, surjectivity means the range is equal to the codomain.
Aug
19
comment Injection, Surjection, Bijection (Have I done enough?)
A couple of comments; firstly, you wrote the definition of injection incorrectly (the word "unique" is missing), and secondly, surjectivity has nothing to do with continuity (although $f$ is indeed continuous). Saying that the range is $\mathbb{R}$ is the same thing as saying that $f$ is surjective.
Aug
19
comment A basic question on linear maps between vector spaces
@prasenjit You need $T(e_i)=\alpha_1T_1(e_i)+\alpha_2T_2(e_i)$ for all $i$, whereas in your argument the $\alpha$s depend on $i$.
Aug
19
comment Quotient groups and isomorphisms, example
I think it might be better to mark as a duplicate of the question without the finiteness restriction, which changes the flavour of the answers a bit. I also hadn't seen this question before so didn't realize it was (or was likely to be) a duplicate until after answering. I'm inclined to leave my answer here because it has some general statements which don't seem to appear in answers to the duplicate questions.
Aug
19
answered Quotient groups and isomorphisms, example
Aug
16
comment Affine space $A^n$ and definition of difference.
@pppqqq That almost certainly won't be necessary to understand the book - but at least now you know what it's called if you want to find out more.
Aug
16
comment Affine space $A^n$ and definition of difference.
@Randal'Thor No, that was a typo. Thanks for catching it!
Aug
16
revised Affine space $A^n$ and definition of difference.
added 7 characters in body
Aug
16
answered Affine space $A^n$ and definition of difference.
Aug
16
comment Is there a special name for planar graphs, when the outer face has the highest degree?
@RobertIsrael Now you've confirmed my suspicion I can even see why this must be true; add a point in the outer face so the drawing is on the sphere, and then remove one inside a different face. So my worry was correct - there can't be a name for such graphs, because it's not a property of the graph. It is a property of the picture, but I would be surprised if it has been named.
Aug
16
comment Is there a special name for planar graphs, when the outer face has the highest degree?
Isn't it sometimes possible to draw the graph in a different way so that a different face is the outer one? (I guess if you still need the drawing to be planar then the answer might be no, but I'd be a little surprised). In other words I'm concerned that the outer face might not be uniquely determined by the graph, but is a property of the particular drawing.
Aug
16
answered Is 4D visualization necessary?
Aug
13
reviewed Close How to run this matlab code?
Aug
13
reviewed Close $\Sigma$-product and Tychonoff product
Aug
13
answered What are some examples of infinite dimensional vector spaces?
Aug
13
comment Notations that are mnemonic outside of English
I always wondered what socle was supposed to mean!
Aug
13
revised Surjective inclusions in Van Kampen's Theorem
added 15 characters in body; edited title
Aug
13
reviewed Close Give an example to show that a factor ring of an integral domain may be a field
Aug
12
comment how to extend a basis
See pages 8-9 of homepages.warwick.ac.uk/~masbal/LinAlg1011/lectures.pdf for a description and example.