FEBRUARY 27: Wistar Comfort (Wesleyan University), "Some Unresolved
Irresolvability Issues". At Queens College, Tea 3:15 pm, Keily 508; Talk 4:00
pm, Keily 119B.
For information, parking: G. Itzkowitz: zev@forbin.qc.edu, (718)997-5849.
ABSTRACT: Following Edwin Hewitt
(1943), one says that a topological space is resolvable [resp.,
kappa--resolvable] if it admits two [resp., kappa--many] disjoint dense subsets.
I will attempt to summarize several lines of investigation pursued over the
years by many investigators. Sample results due to Malykhin, Protasov, Zelenyuk
and others are: 1. Every infinite Abelian group G not containing the countably
infinite Boolean group contains two disjoint sets, both dense in each
nondiscrete group topology on G. 2. Every infinite group G contains |G|--many
disjoint sets, each dense in each maximally almost periodic group topology on G.
3. Every countably compact, dense-in-itself regular Hausdorff space is
resolvable. The emphasis will be on unsolved problems (the "unresolved
irresolvability issues"). Remark. My own efforts will be cited as time permits.
Co-authors include Jan van Mill, Li Feng, Oscar Masaveu, Hao Zhou, Salvador
Garcia-Ferreira, and Wanjun Hu.
MARCH 6: No seminar.
MARCH
13: Melvin Henriksen, "A survey of what we know and don't know about
spaces X for which the ring C(X) of continuous real-valued functions has a
compact space of minimal prime ideals". At Baruch College, Tea 3:15 pm, Talk
4:00 pm, Conference Room (6-215), Mathematics, 6th floor, Vertical Campus,
Lexington Avenue and 24th Street.
Contact: A. R. Todd: artbb@cunyvm.cuny.edu, (646) 312-4136.
ABSTRACT: There are
characterizations of such spaces that are not easy to use. This class includes
all metrizable and all separable spaces, but not all that are first countable.
The Stone-Cech compactification betaD of discrete space D has this property has
this property, but betaD \ D does not if D is infinite Topics like when this
property is finitely productive, what kinds of subspaces inherit it, and under
what kinds of mappings it is preserved are discussed. There are lots of open
questions.
MARCH 20: No seminar -- Spring Topology Conference in
Texas!
MARCH 27: Ralph Kopperman, "Two applications of bitopological complete
regularity to theoretical computer science". At College of Staten Island;
Tea 3:15 pm, 1S/215, Talk 4:00 pm, 1S/112.
Contact: P.R. Misra, (718-982-3626),prmisra@netzero.net.
ABSTRACT: We discuss characterizations of
bitopological complete regularity, and their role in the solution of the computational
model problem, as well as in the existence of pmetrics. The latter measure distance and
size simultaneously, and are important in the study of partial computations.
APRIL 3: Jyotirmoy Sengupta (Tata Institute of Fundamental Research, Bombay, India),
"The uncertainty principle on Riemannian symmetric spaces of the noncompact type".
At College of Staten Island; Tea 3:15 pm, 1S/215, Talk 4:00 pm, 1S/112.
Contact: P.R. Misra, (718-982-3626),prmisra@netzero.net.
ABSTRACT: Heisenberg's famous uncertainty
principle in quantum mechanics says that it is impossible to simultaneously determine
the position and momentum of a particle. The mathematical version of this principle is
the paradigm which says that it is impossible for a function and its Fourier transform
to be simultaneously very rapidly decreasing. The talk will be survey of recent results
in this area with emphasis on the case of Riemannian symmetric spaces of the noncompact type.
APRIL 10: Vladimir Tkachuk (Mexico), "Factorization theorems: their power and some
simple proofs". At College of Staten Island; Tea 3:15 pm, 1S/215, Talk 4:00 pm, 1S/112.
Contact: P.R. Misra, (718-982-3626), prmisra@netzero.net.
APRIL 16 - APRIL 24: Spring Break!
MAY 1: Gerald Itzkowitz, "On Sigma Spaces". At Brooklyn College; Tea 3:15 pm, Talk 4:00 pm,
Ingersoll Hall 1146, Mathematics Department. Contact: R.Z. Bouziakova, (718-951-5833),
RaushanB@brooklyn.cuny.edu.
MAY 8: Don Johnson, "Spaces of Prime Initial Sets". At Baruch College;
Tea 3:15 pm, Talk 4:00 pm, Conference Room (6-215), Mathematics,6th floor, Vertical Campus,
Lexington Avenue and 24th Street. Contact: A. R. Todd, (646-312-4136),
artbb@cunyvm.cuny.edu.
ABSTRACT: For commutative semigroups,
prime ideals minimal among all primes containing a fixed ideal were characterized
by J. Kist in a 1963 paper, where it was shown that families of such minimal prime ideals
form zero-dimensional spaces when provided with the hull-kernel topology. Here, we consider
the analogous condition for initial sets in preordered sets: it is sufficient for minimality
of a prime initial among all prime initials containing a fixed initial, but it is not necessary.
An example of an ordered set is presented that has spaces of such minimal prime initials
having widely varying topological properties, including one that is connected Hausdorff.
Also, a construction is presented which shows that every T-zero space can be represented
as a space of prime initial sets (with the hull-kernel topology) of some ordered set.
This provides an example of a zero-dimensional space of prime initials, no one of which is
minimal.
This work, which is joint with J. Kist, will appear in the Proceedings of the 2001 New York
Summer Topology Conference.
MAY 15: Raushan Buzyakova, "On hereditary D-property of Cp over compacta".
At Brooklyn College; Tea 3:15 pm, Talk 4:00 pm, Ingersoll Hall 1146, Mathematics Department.
Contact: R.Z. Bouziakova, (718-951-5833),
RaushanB@brooklyn.cuny.edu.
ABSTRACT: A mapping \phi from X to the topology
of X is called a neighbourhood assignment on X if x\in \phi (x) for all x. A space X is called
a D-space if for any neighbourhood assignment \phi on X there exists a closed discrete
D\subset X such that the union of \phi (d)'s, where d\in D, covers X. It will be shown that
Cp over compacta has the above property hereditarily. This result, in particular,
implies the Baturov theorem as well as Grothendieck theorem for compacta. Some open questions
connected with this result will be raised.
For more information, contact:
CCNY: R. Kopperman (on leave)
College of Staten Island (718 982--3626): P.R.Misra
Baruch College (646 312-4136) A.R.Todd
LIU C. W. Post Center (516 299-2447): S. Andima
Queens College, Math. (718 997-5849): G. Itzkowitz
Marymount College (914 631-3200): M. Hastings
Queens College, Comp. Sci. (718 997-3478): T. Y. Kong
Brooklyn College (718-951-5833): R. Z. Bouziakova