…“Would you tell me, please, which way I ought to go from here?”
“That depends a good deal on where you want to get to,” said the Cat.
“I don't much care where” said Alice.
“Then it doesn't matter which way you go,” said the Cat.
“so long as I get somewhere,” Alice added as an explanation.
“Oh, you're sure to do that,” said the Cat, “if you only walk long enough.”
Alice felt that this could not be denied…
.?...|
..)e.+#
....%|
If I were a NetHack monster, I would be a floating eye.
I see and sense absolutely everything that happens around me.
I just don't do very much about it.
programmern. an active entity, typically a human, that writes a
program, and that might or might not also be a user of the
program. (From the Common
Lisp HyperSpec.)
Address
Classe di Scienze – Scuola Normale Superiore
Piazza dei Cavalieri, 7, 56126 Pisa (PI) – Italy
Arithmetic of Dedekind cuts on ordered Abelian groups
(with A. Fornasiero) (Annals of Pure and Applied Logic 156 (2008) 210–244,
DOI:10.1016/j.apal.2008.05.001).
We study the set of Dedekind cuts over a linearly ordered Abelian group as a structure over the language (0,<,+,-).
Moreover, we obtain a simple set of axioms for the universal part of the theory of such structures.
Finally, we prove that every structure satisfying the given axioms is a sub-structure of the set of cuts over a suitable group.
Higher homotopy of groups definable in o‐minimal structures
(with A. Berarducci & M. Otero) (to be published in the Israel Journal of Mathematics).
It is known that a definably compact group G is an extension
of a compact Lie group L by a divisible torsion‐free normal subgroup. We show
that the o‐minimal higher homotopy groups of G are isomorphic to the
corresponding higher homotopy groups of L. As a consequence, we obtain that all
abelian definably compact groups of a given dimension are definably homotopy
equivalent, and that their universal cover are contractible.
On the homotopy type of definable groups in an o‐minimal structure
(with A. Berarducci) (submitted).
Given a definably compact group G in a saturated o‐minimal structure, there is a canonical homomorphism from G to a compact real Lie group F(G). We establish a similar result for the (o‐mininimal) universal cover of a definably compact group. We also show that F(G) determines the definable homotopy type of G. A crucial step is to show that the fundamental group of an open subset of F(G) is isomorphic to the definable fundamental group of its preimage in G. Our results depend on the study of the o‐minimal fundamental groupoid of G.
Splitting definably compact groups in o‐minimal structures (submitted).
An argument of A. Borel shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an o‐minimal expansion of a real closed field. As opposed to the Lie case, however, we provide an example showing that the derived subgroup may not be a semidirect factor of the group.
Stuff
If you want to use Xboard
as an ICS client with a nice coloured
and customisable dialog window, then you may want to try the good old
jennifer.c (modified by Paolo Casaschi, still needs a rewrite).
If you like playing on FICS,
but you don't like running
timeseal
(for example because no one knows what it actually does), than the good old
openseal is the hack for you (works on linux and Mac OS X,
has been reported to work on freebsd, and should do on any unix).
Connected to the previous item, here
is the server side version of openseal, designed to work with
this avatar of the lasker
open‐source chess server (the maintainer of which, however, bears no responsibility
for my crimes).
Compass
(jad, jar,
source)
is a little MIDlet I wrote, originally to compute the rising and setting times
of the Sun. Turned out that I changed my mind while writing it, and now its
purpose is to display the needle of a compass on the monitor of your cell
phone, angled so that it points North whenever the keyboard of your phone
points toward the Sun. As a byproduct, it can compute the rising, transit, and
setting times of the Sun.
