FEBRUARY 16: Ralph Kopperman, CCNY, "On storage of topological
information". At the Graduate Center. Talk 4:15, 9204/9205; wine and
cheese reception after, 4102 (Science Center). More information can be
found at
http://web.gc.cuny.edu/Computerscience/cs_cllqm/colloquiumschedule.htm.
ABSTRACT:
We live in a topological space, and often information about some
topology is used for reasons that are scientific or technical (eg., CAD or
pattern recognition), or simply for entertainment. We discuss a way to
store and use such information which may avoid round off issues common to
some other methods.
MARCH 30: V. V. Tkachuk, UAM, Mexico City, will discuss "A quest for
duality with respect to neighbourhood assignments," at Queens College, Tea
3:15 in Kiely 508, talk 4:00 in Kiely 334. For local information and
parking, contact G. Itzkowitz 718-997-5849,
gitzkowitz@prodigy.net.
ABSTRACT: Given a space X a family {\bf O}=\{Ox:x\in X\} is a
neighbourhood assignment in X if Ox is an open neighbourhood of
x for any point x\in X. A set K\subset X is a kernel of \bf O
if \bigcup\{Ox:x\in K\}=X. We will say that X is dually \bf P
if any neighbourhood assignment in X has a kernel with the property \bf P.
We study how the duals behave for compact-like properties \bf P.}
APRIL 20: Homeira Pajoohesh, City College of New York, "How derivations
on a ring help us to understand its properties." At CW Post. Tea in
Room 238 at 3:15; lecture at 4:00, room TBA. For parking and more information,
contact S. Andima, sandima@liu.edu.
ABSTRACT: Consider the usual derivative
operator ' on the ring of differentiable functions. It is additive and (fg)'=f'g+fg'.
This definition has been generalized: for every ring R, a derivation
d on R is an additive function such that d(ab)=d(a)b+ad(b). Positive
derivations on rings with an order are those such that whenever an element
is positive, its derivation is positive. We investigate the properties of
positive derivations on the lattice ordered rings of matrices and
characterize some of these rings by their positive derivations.
APRIL 27: Jerzy Kakol, Poznan, Poland: "Lindel{\"o}f spaces C(X) over
topological groups." At Baruch College Vertical Campus, Lexington Avenue and 24th
Street; Tea 3:15 Room 6-215, talk 4:00 Room 6-215. For local information, contact
A. Todd, artbb@cunyvm.cuny.edu .
ABSTRACT: One of the unsolved problems
in theory of spaces Cp(X) asks when exactly for a given X the
space Cp(X) is Lindel{\"o}f. It is well-known that, for example,
if X is second countable, then Cp(X) is Lindel{\"o}f.
The same conclusion holds also for (not necessarily second countable) Corson compact
spaces X (Alster-Pol-Gul'ko's theorem).
We solve this problem for locally compact group.
Several equivalent conditions for Cp(X) to be Lindel{\"o}f when
X is a locally compact group are provided . One shows (among the others) that
for a locally compact topological group X the following assertions are equivalent:
(i) X is metrizable and \sigma-compact.
(ii) Cp(X) is analytic.
(iii) Cp(X) is K-analytic.
(iv) Cp(X) is Lindel{\"o}f.
(v) Cc(X) is a separable metrizable complete locally convex space.
(vi) Cc(X) is compactly dominated by irrationals. If additionally X
is an additive and abelian locally compact group, then Homp(X) (the
group of continuous characters on X endowed with the pointice topology)
is K-analytic iff X is metrizable. This result supplements earlier
results of Corson, Christensen and Calbrix and provides several
applications, for example, it easily applies to show that:
(1) For a compact topological group X the Eberlein, Talagrand,
Gul'ko and Corson compactness are equivalent and any compact group of this
type is metrizable.
(2) For a locally compact topological group X the space Cp(X) is
Lindel\"of iff Cc(X) is weakly Lindel{\"o}f. The proofs heavily depend
on the following result of independent interest which seems not to be
noticed so far: A locally compact topological group X is metrizable iff
every compact subgroup of X has countable tightness. More applications
are provided.
MAY 4: Thierry Vallee, UC Cork, Computer Science:
"Compatible topologies on graphs: an application to Graph Isomorphism problem Complexity."
At the CUNY Graduate Center Computer Science Colloquium. Talk 4:15 - 5:30 p.m., Room 9204-5.
Tea following the talk, Room 4102.
ABSTRACT: In one hand the graph isomorphism problem (GI)
has received considerable attention due to its unresolved complexity status and its
many practical applications. In the other hand a notion of compatible
topologies on graphs has emerged from digital topology.
In this talk we study GI from the topological point of view.
Firstly we explore the poset of compatible topologies on graphs and in particular on
bipartite graphs. Then, from a graph we construct a particular compatible
Alexandroff topological space said homeomorphic-equivalent to the graph.
Conversely from any Alexandroff topology we construct an
isomorphic-equivalent graph on which the topology is compatible. Finally
using these constructions, we show that GI is polynomial-time equivalent
to the topological homeomorphism problem (TopHomeo). Hence GI and TopHomeo
are in the same class of complexity.
MAY 11: Richard G. Wilson, UAM, Mexico City:
"Complete accumulation points of discrete sets." At College of Staten Island;
tea 3:15 in 1S/215, talk 4:00 in 1S/112. For local information and parking, contact
P. R. Misra, prmisra@netzero.net .
ABSTRACT: A classical theorem of General
Topology states that a Hausdorff space is compact if and only if each infinite subset
has a complete accumulation point. Additionally, it is known that a Hausdorff space
is compact if and only if the closure of every discrete subspace is compact. On
comparing these results, it is natural to ask whether one can characterize compactness in
terms of complete accumulation points of discrete sets.
Question: Is it true that if every discrete subspace of
a Hausdorff space X has a complete accumulation point in X, then X
is compact? We will discuss the answer to this question in the talk.
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. (718-380-1832): G. Itzkowitz
Queens
College, Comp. Sci. (718-997-3478): T. Y. Kong