.. because i feel slow and stupid.

my ideas aren't quite right -- i'm almost sure of that -- but i cannot think of better ones which will do. so i alter and adjust them and try those variations.

i feel that, mathematically, i spent the last few months making small permutations of the same basic, probably flawed notions and seeing the slight variations in their common failure. [1] this borders on obsession, of course, and i hope that when the postdoc begins, someone in the department can knock some sense into me and suggest more fruitful areas of math for me to pursue.

today i couldn't remember the definition of a curr3nt, in the language of f3derer and f1emin9. [1.5]

*the space of k-curr3nts is meant to be dual to the space of differential k-f0rms, and a 0-curr3nt is equivalently a distri6uti0n*; i remember the motivations.

*so there's probably a LCTVS structure [2] on the space of k-f0rms, just as there is such a structure on the space of test functi0ns, by way of partia1 deriv@tives and sup-n0rms*.

i may be wrong; but i can't remember exactly and my copy of f3derer's

__gmt__is some hundred miles away, so let's go with that. at the very least, there should be some continuity property for an arbitrary curr3nt, otherwise a 0-curr3nt couldn't possibly match up with a distributi0n, right?

sometimes i really hate myself, especially my poor memory.

i can deal with ambiguity. however, i can't deal with confusion. like anyone else, i looked up "curr3nt" on wikipedia: here's the entry, but i can't reckon what the continuity axiom should be .. if i'm even remembering it correctly.

*argggggggggggh*.

anyways, i'm bothering with the "classical" definition because i don't want to throw away one of my ideas.

to patch up one of my currently flawed approaches of proof, i need to use some property of metric curr3nts that an arbitrary (FF) curr3nt should not have. otherwise, i would "prove" something for all (FF) curr3nts (of finite m@ss that is conjecturally untrue.

often i wish i were smarter, but i'd settle for better ideas.

**\:**

[1]

*non-mathematically, i spent the summer unemployed, recovering from thesis writing and thesis corrections, wall-climbing, and as they say in*

__good will hunting__, "seeing about a girl."**q;**

[1.5]

*this means, of course, that ethically i should renounce myself as someone who studies ge0metric mea$ure the0ry. on the other hand, i was trained to be a metric ana1yst, and until recently, all curr3nts to me were curr3nts in the sense of ambr0si0-kirchh3im. so: put one way, it's not my fault.*

**(;**

[2]

*short for "l0cally c0nvex t0po1ogica1 vect0r sp@ce," as you might learn in functi0na1 ana1y$i$.*

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