OCTOBER 3: Steve Saxon (University of Florida at Gainesville), "Some
problems connecting Banach and barrelled spaces". At Baruch College. Tea
3:15 pm, Talk 4:00 pm, Conference Room, Mathematics Department, 6th floor,
Vertical Campus, Lexington Avenue and 24th Street. Contact A. R. Todd,
(646) 312-4136, artbb@cunyvm.cuny.edu.
ABSTRACT: The separable quotient (SQ) problem asks if every
infinite-dimensional Banach space has a proper separable quotient, and
apparently has remained unanswered in the seventy years since Banach's
time. Twenty-five years ago Saxon and Wilansky showed that a Banach space
has a proper separable quotient if and only if it has a dense nonbarrelled
subspace, necessarily of uncountable codimension, equating the SQ problem
with a barrelled space problem. This talk focuses on this surprising
connection between a longstanding unsolved problem and barrelled spaces.
It also brings the story up-to-date.
OCTOBER 17: Oleg Okunev (Ottawa, Canada), "On separable surlindelof
compact spaces". At Brooklyn College. Tea 3:15 pm, Talk 4:00 pm, Ingersoll
Hall 1146, Mathematics Department.
OCTOBER 24: Mary Ellen Rudin (U. of Wisconsin at Madison), "Two favorite
(totally unsolved) problems: The Linearly Lindelof problem and the Point
countable base problem". At Brooklyn College. Tea 3:15 pm, Talk 4:00 pm,
Ingersoll Hall 1146, Mathematics Department.
OCTOBER 31: Jerzy Kakol, Adam Mickiewicz U. and Baruch College,
"On countable bounded tightness for space
Cp(X)". At Baruch College.
(For times, room and contact, please see October 3.)
ABSTRACT: It is well-known that the space Cp([0,1]) has countable
tightness but is not Frechet-Urysohn. Let X be a Cech-complete
topological space. We prove that the space Cp(X) of continuous
real-valued functions on X endowed with the pointwise topology is
Frechet-Urysohn if and only if Cp(X) has countable bounded tightness,
that is, for every subset A of Cp(X) and for every f in the closure
of A in Cp(X), there exists a countable and bounding subset of A
whose closure contains f. (Joint research with M. Lopez-Pellicer).
NOVEMBER 7: Raushan Buzyakova, "On relative topological properties". At
Brooklyn College. Tea 3:15 pm, talk 4:00 pm, Ingersoll Hall 1146,
Mathematics Department.
NOVEMBER 14: Aaron R. Todd, Baruch College, CUNY, "A functional analytic characterization of
pseudocompact spaces (Warner bounded spaces)". At Baruch College. Tea 3:15 pm, Talk 4:00 pm,
Conference Room (6-215), Mathematics Department, 6th floor, Vertical Campus, Lexington Avenue and
24th Street. Contact: A. R. Todd, (646) 312-4136, artbb@cunyvm.cuny.edu.
ABSTRACT: E=Cc(X) is the space of realvalued functions continuous on a T3.5-space X with
the compact-open topology, and E' is the space of continuous linear functionals on E.
We discuss a first principles proof of the equivalence of spaces in the title and a plenitude
of infinite dimensional bounded subsets of the dual E' with its weak topology, \sigma(E',E),
(strong topology, \beta(E',E)). We are aided by a sequential characterization of Warner
boundedness that reveals it to be a generalization of \omega-boundedness.
NOVEMBER 21: No seminar. Check with Aaron Todd about public lecture at Baruch.
NOVEMBER 28: Thanksgiving.
DECEMBER 12: Prabudh R. Misra, "Zero Sets in \beta X". At Brooklyn College. Tea 3:15 pm,
Talk 4:00 pm, Ingersoll Hall 1146, Mathematics Department. Contact: R. Z. Bouziakova,
(718) 951-5833.
ABSTRACT: When X is pseudocompact, it is well known that the closure in /beta X of any
zero-set of X is a zero-set in /beta X. We will discuss the corresponding situation when X is
a metric space.
FOR MORE INFORMATION, CONTACT:
CCNY: R. Kopperman (on leave): rdkcc@cunyvm.cuny.edu.
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.
Baruch College (646 312-4132) J. Kakol.