Recent content by Adriadne

Phew! Thanks George, I was beginning to think I should study sociology instead.

Then I give up! If there's no agreed definition, only a general agreement that we don't need to specify (even to a beginner) whether we're talking about fields, spaces or vectors, then it's a lost cause. I'm really cross! (but only at myself). Thanks all for trying.

So, I have from Hurkyl (I paraphrase, I hope accurately): A 1-form is a dual vector field and is a tensor. Implication: a tensor is a vector field. From George: I agree, but don't worry, we can evaluate the 1-form = dual vector field, at the point P, and get our linear functional as usual...

Jimmy, thanks for that. Last things first (as always!). My Dover edn. of Schutz's book has indeed corrected that typo. Had it not, I would have binned it by now. But to return to the core of my problem. Schutz, you, me have no problem in thinking about a vector space T*p at P which is dual...

Sorry guys, I was being really stupid. Of course elements of T on X are subsets of X (they are also subsets of T, as T is a set of sets, as I said). What Iwas getting at was that the partition of X for the topology may be quite different from the partition which generates "natural" subsets, but...

No, a (a point) is an element in X. {a} is a singleton set, not a point Yes (in your topology) Yes it is, in your topology No, see (1) Yes No, a is an element in X Yes, an element in T Emphatically no (double braces indicate set of sets. T contains as its fewest elements X and {}) As above...

Hey are you serious? If I have a set X with elements a, b and c, I'm going to to write X = {a,b,c}. a is an element of X, not a subset, that makes no sense. Remember, T is a set of sets, {a} is only a set ( a singleton) in T, not X.

Jimy, don't be silly, you helped me loads. Thanks

Yep, figured that later, thanks Yep, got that too, also after. Thank you so much.

George, no. A might possibly be subset X (but I don't think it need be - consider the quotient topology for e.g.) The point is that the topology T on X is a set of sets, like the set X = {a,b,c}, a possible topology T on X = {X {} {a} {b,c}}. Here, evidently {b,c} may be subset X but a is an...

I posted this on another forum, but had no response. Maybe because it's too stupid the bother with? Anyway... Say I have a set X and a topology T on X so that T = {X {} A} i.e A is an open subset of T. Then the complement of A is Ac = X - A, which is closed. Now the interior of A, int(A) is...

mm. My Schutz is Geometrical methods of mathematical physics I suspest you're reading his GR Why sure. The problem I had, and have only resolved in a Micky Mouse way (with help here) is that Schutz introduces 1-forms as a dual space at the point P, whereas George and Hurkyl say they are a...

Thanks George (you too Hurkyl), that's helpful. I particularly like the notion of a field being a cross section of a bundle.

George, thanks, I appreciate your efforts, but you'll have to forgive me being a little slow here. Let's see if there's an early flaw in my thinking: In any generalised space, a vector space V at the points P, Q... is all vectors at P, Q... (Yes, I'm aware this is a hokey definition of a...

OK, that's progress for me, thanks. Nevertheless, I still don't quite see how I can turn a field (one thingy per point in space) into a space (all thingys at a point in space). Schutz (and Flanders I now see) insist that one-forms inhabit a vector space. If I want to think about all spaces at...