MARCH 31: Ralph Kopperman, CCNY, "Approximation of
compact Hausdorff spaces by finite spaces and a theorem in Gillman and Jerison".
At College of Staten Island. Tea 3:15 at 1S/215, talk 4:00 at 1S/112. For
parking contact P. R. Misra, (718)982-3626, prmisra@netzero.net.
ABSTRACT:
Every compact Hausdorff space is the subspace of closed points of an inverse
limit of finite T0 spaces (but the 0-dimensional ones are those which
are subspaces of inverse limits of finite T1 spaces).
This inverse
limit is not itself Hausdorff, but is compact, and it can be chosen so that all
its compact subspaces are normal. This is shown using the fact that the set of
prime ideals containing a given prime ideal is always a chain (under set
inclusion), 14.8 of Gillman-Jerison, originally due to Kohls.
APRIL
7: David M. Clark, SUNY at New Paltz, "Axiomatizability of
Topological Quasi-varieties". Tea 3:15, talk 4:00, at C. W. Post. For parking
and more information, contact Susan Andima, mailto:sandima@liu.edu.
ABSTRACT:
A topological quasi-variety X is a category obtained from a discrete finite
algebraic structure M by closing {M} under formation of direct products,
topologically closed substructures and isomorphic images. The resulting category
X=ISP(M) contains certain algebraic structures of the same type as M with a
compatible Boolean topology. Much effort has gone into a search for axiomatic
descriptions of specific topological quasi-varieties. We find that, for a finite
structure M, there are exactly three possibilities: among Boolean topological
structures, X either consists of all models of its underlying universal Horn
theory, of all models of some first order theory but of no universal theory, or
it is not first order definable at all.
Illustrations of
these three options will be drawn from groups, rings, semigroups, lattices,
orders, and graph colorings.
APRIL 14: Homeira
Pajoohesh, CEOL, University College Cork, IE, "Completions of Partial Metrics."
Tea 3:15, talk 4:00, at a venue to be
arranged.
ABSTRACT: Partial
metrics are metrics except that the distance from a point to itself need not be
0; this property is needed to model the partial information obtained in
computation. Each partial metric gives rise to two topologies, and if we allow
their values to lie in a power of the unit interval, there is always a partial
metric that gives rise to the Scott and lower topologies on continuous posets,
which are important in the denotational semantics of computing. Partial metric
spaces have both a metric completion, and a spherical completion, and we discuss
both.
No meetings April 21 or 28.
For more
information, contact:
CCNY (212-650-5346): R. Kopperman
College
of Staten Island (718-982-3626): P. R. Misra
Baruch College (212-387-1463):
A. Todd
LIU C. W. Post Center (516-299-2447): S. Andima
Marymount College
(914-631-3200): M. Hastings
Queens College, Math. (718-997-5849): G.
Itzkowitz
Queens College, Comp. Sci. (718-997-3478): T. Y.
Kong