NOVEMBER 9: Mini-Conference on Set Theoretic Topology in Functional Analysis
and Topological Groups at BARUCH COLLEGE.
This mini-conference is organized with the New York Seminar on General
Topology and Topological Algebra at Baruch College, CUNY. It addresses
uses of set theoretic topology in topological vector spaces, functional
analysis, and topological groups.
The mini-conference begins with the regular New York Topology Seminar,
Thursday afternoon, November 9, 2006, with tea at 3:15 p.m. in the
Baruch College Department of Mathematics, sixth floor of Baruch
College's Vertical Campus at Lexington Avenue between 24th and 25th
Streets. At 4pm, the Seminar meets:
November 9, 4pm: Stephen A. Saxon, Gainesville (USA), "Quasi-Suslin
weak duals".
The conference continues Saturday, November 11th at the same site.
Longer Talks---Speakers and Titles:
Jerzy Kakol, Poznan (Poland), "K-analyticity and Compact Coverings".
M. Lopez Pellicer and S. Moll, Valencia (Spain), "About the
Talagrand-Tkachuk Theorem".
Shorter Talks---Speakers and Titles:
J. C. Ferrando, Elche (Spain), "On quasi-Suslin spaces and related
topics".
Arkady Kitover, Philadelphia, "Topological dynamics and operators
without invariant sublattices".
If you think you might participate and/or contribute a talk, please
contact one of the organizers below as soon as possible:
Aaron R. Todd (artodd@panix.com)
Ralph Kopperman (rdkcc@ccny.cuny.edu)
ABSTRACTS
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J.C. Ferrando, Centro de Investigacion Operativa, Universidad Miguel
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ABSTRACT: This talk is devoted to go over quasi-Suslin spaces from the
point of view of their relations with some classes of topological
spaces considered in descriptive set theory and used in Functional
Analysis, such as K-analytic spaces, Lindel\"of \Sigma-spaces,
web-compact spaces and trans-separable spaces.
BIBLIOGRAPHY
Arkhangel'skii, A.V., "Topological function spaces".
Math. and its Applications 78. Kluwer Academic Publishers. Dordrecht Boston
London, 1992.
Cascales, B., "On K-analytic locally convex spaces".
Arch. Math 49 (1987), 232-244.
Ferrando, J.C., Kakol, J., Lopez Pellicer, M. and
Saxon, S.A., "Quasi-Suslin weak duals". J. Math. Anal. Appl., to appear.
Martineau, A., "Sur des theor`emes de S. Banach
and L. Schwartz concernant le graphe ferme". Studia Math. 30 (1968), 43-51.
Nakamura, M., "On quasi-Suslin spaces and closed graph
theorem". Proc. Japan Acad. 46 (1970), 514-517.
Nakamura, M., "On K-Suslin spaces".
Proc. Japan Acad. 47 (1971), 705-706.
Orihuela, J., "Pointwise compactness in spaces
of continuous functions". J. London Math. Soc. 36 (1987), 143-152.
Robertson, N., "The metrisability of precompact sets".
Bull. Austral. Math. Soc. 43 (1991), 131-135.
Rogers, C.A., "Analytic sets in Hausdorff spaces".
Mathematika 11 (1968), 1-8.
Tkachuk, V.V., "A space Cp(X) is dominated
by irrationals if and only if it is K-analytic". Acta Math. Hungar. 107 (2005),
253-265.
Talagrand, M., "Espaces de Banach faiblement K
-analytiques". Ann. Math. 110 (1979), 407-438.
Valdivia, M., "Topics in locally convex spaces".
Notas de Matematica 67, North Holland. Amsterdam New York Oxford, 1982.
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Jerzy Kakol, Poznan (Poland), "K-analyticity and Compact Coverings".
______________________________________________________________________________________________
ABSTRACT: It is known by a result due to Talagrand and Preiss that
every Weakly Compactly Generated Banach space E (shortly WCG Banach
space) is weakly K-analytic, i.e. K-analytic in the weak topology of
E. Also due to Amir-Lindestrauss every WCG Banach space E enjoys
the following applicable property: dens(E)=dens(E',\sigma(E',E)). By
a famous Amir-Lindestrauss theorem for a compactum K the space C(K)
is WCG iff K is Eberlein compact, i.e. is homeomorphic to a weakly
compact subset of some Banach space. This yields that if C(K) is WCG,
then Cp(K) is K-analytic. These concrete situations motivated
several specialists to study analyticity and K-analyticity in
functional analysis in some more general setting. The aim of my talk is
to present a natural extension of these results, some ideas from
descriptive set topology related with K-analytic spaces, analytic
spaces, quasi-Suslin spaces to study concrete problems from functional
analysis.
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Arkady Kitover, Philadelphia, "Topological dynamics and operators
without invariant sublattices."
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ABSTRACT: Using some recent results in topological dynamics, A.W.
Wickstead and the presenter constructed examples of positive weighted
composition operators in C(K) and L^p without closed invariant
sublattices.
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M. Lopez Pellicer and S. Moll, Valencia (Spain), "About the
Talagrand-Tkachuk theorem".
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ABSTRACT: Talagrand proved that if X is a compact Hausdorff space,
then the space C{p}(X) of continuous real valued functions on X
with the pointwise topology is K-analytic if and only if it is
dominated by irrationals, that means C{p}(X) is covered by a family
\{K{\alpha}: \alpha \in N^{N}\} of compact sets such that
K{\alpha} \subset K{\beta} for \alpha \leq \beta.
Very recently this remarkable result has been extended by Tkachuk to any completely
regular Hausdorff topological space X. The aim of this talk is to
present some applications of the Tkachuk result and provide some ideas from
the descriptive set topology to clarify the main proof given by
Tkachuk. The Baturov and Okunev theorems applied by Tkachuk in his
original proof will be discussed.
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Stephen A. Saxon, Gainesville (USA), "Quasi-Suslin weak duals".
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ABSTRACT: This talk is about joint work with Professors Ferrando,
Kakol, and Lopez-Pellicer. In our previous paper, we showed that if a
locally convex space is in a certain subclass of \fractur {G}
(introduced by Cascales and Orihuela), then its weak dual is
quasi-Suslin, and asked if the result is true for all of class \fractur
{G}. In a paper just submitted that bears the title of this talk, we
are able to give an affirmative answer. Several other advances in this
area between analysis and topology are made, as well. For example, a
countably tight locally convex space remains countably tight under its
weak topology provided its weak dual is quasi-Suslin, and our examples
show this is two levels of generality better than than the corresponding
Cascales/Kakol/Saxon result (2002), itself a vast extension of the
original Kaplansky result for metrizable locally convex spaces. We also
prove that when the weak dual is quasi-Suslin, a locally convex space
is countably tight under its weak topology if and only if the weak dual
is K-analytic.
NOVEMBER 16: Denis Blackmore, New Jersey Institute of Technology,
speaks on "Equivalence of Computational Geometric Objects", at CCNY.
Tea 3pm, NAC 8/133, talk 4pm.
ABSTRACT: The category of Whitney regular stratified varieties is
introduced and shown to be ideal for the geometric objects arising in
the nascent field of computational topology. In particular, we show
that these objects have analogs of tubular neighborhoods (so useful
for manifolds in differential topology), which can be employed to
resolve a number of important questions regarding their topology. To
illustrate our current joint work with Ralph Kopperman and Tom Peters,
we describe how these tubular neighborhoods can be used to prove the
embedding and ambient isotopic equivalence of geometric objects, and
provide a structure that facilitates the algorithmic computation of
their homology and cohomology in conjunction with either simplicial
or non-Hausdorff space approximations.
DECEMBER 19 : Lewis D. Ludwig, Denison University, "Linking in straight-
edge embeddings of K7". At CSI; tea 3:15 1S/215, talk 4:00 1S/112. For
parking contact P. R. Misra, (718)982-3626,
prmisra@gmail.com.
ABSTRACT: In 1983 Conway and Gordon
and Sachs proved that each embedding of the complete graph on six vertices, K6,
is intrinsically linked. That is, every embedding of K6 contains at least one link.
Because of the applications of knot theory and graph theory to the field
of chemistry and the synthesis of knotted and linked molecules, Hughes
and Caragiu independently proved that all straight-edge embeddings of
K6 have either one or three (3-3) links. We have extended this work to
characterize all (3-3) links and (3-4) links in any straight-edge embeddings
of K7. No prior knowledge of knot theory is assumed for this 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
Queens College, Math. (718-380-1832):
G. Itzkowitz
Queens College, Comp. Sci. (718-997-3478): T. Y. Kong