FEBRUARY 19: Ralph Kopperman, CCNY. "The relationship of its separation
and connectedness to the finite approximation of a topological space by finite
$T_0$-spaces". At CCNY. Tea 3:15, NAC 8/133; talk 4:00 NAC 8/133. For
information contact R. Kopperman, rdkcc@cunyvm.cuny.edu.
ABSTRACT: It has long been known
that the T1-spaces are those which are subspaces of a space of closed points in
an inverse limit of finite T0-spaces and continuous maps. Richard Wilson and the
speaker have recently obtained several results about the relationship between
the separation properties of the space and properties of the maps and the
inverse system. Further, an inverse limit of connected finite T0-spaces is
connected.
FEBRUARY 26: Nataniel Greene, SUNY at Stony Brook. "New
Methods for Overcoming the Gibbs Phenomenon". Tea 3:15, talk 4:00, Room 6-215
Baruch Coll. Vertical Campus, Lexington Av. and 24 St. For information contact
A. Todd, artbb@cunyvm.cuny.edu.
ABSTRACT: Fourier and orthogonal
polynomial approximations of analytic functions are known for their exponential
accuracy, and in general the accuracy of the approximation increases with the
number of derivatives a function has. This is referred to as as spectral
accuracy.
However, the Fourier and orthogonal polynomial
expansion of a piecewise smooth function will fail to converge at the points of
discontinuity. Furthermore, spurious oscillations will infect the entire domain,
limiting the global accuracy away from the points of discontinuity. This
behavior is known as the Gibbs phenomenon.
We describe a
new theory developed by this author for overcoming the Gibbs phenomenon. This
new theory allows for the global recovery of a piecewise smooth function without
the need for any edge detection. It also applies to approximations in more
general expansion bases and integral transforms which suffer from the Gibbs
phenomenon, such as wavelets.
MARCH 4: Steve Saxon, U. of Florida. "Warner bounded analyses/analogies".
Tea 3:15, talk 4:00, Room 6-215 Baruch Coll. Vertical Campus, Lexington Av. and 24 St.
For information contact A. Todd, artbb@cunyvm.cuny.edu.
ABSTRACT: An important feature of many
locally convex topological vector spaces is a fundamental sequence of bounded sets (fsbs);
e.g., all df-spaces and DF-spaces. Warner proved that a T3½-space
X is Warner bounded if and only if Cc(X), the space of
continuous real-valued functions on X endowed with the compact-open topology,
has a fsbs. He gave several other equivalent conditions. We (Jerzy Kakol, Aaron Todd and myself)
give much simpler arguments by first showing that X is Warner bounded if and only if
Cc(X) does not contain a linear and topological copy of a dense subspace
of the product space RN. As a consequence, additional analytic
characterizations become readily available. A number of their analogs very nicely characterize
when X is pseudocompact, and when Cc(X) is a df-space,
the latter amply answering Jarchow's 1981 question. For example, we find that X is
pseudocompact if and only if Cc(X) does not contain a copy of
RN, and Cc(X) is a df-space if and only if
its strong dual is a Banach space. Another example: X is pseudocompact, X is
Warner bounded, or Cc(X) is a df-space if and only if for each
sequence (µn)n\subset Cc(X)' there exists
a sequence (\epsilonn)n\subset(0,1] such that
(\epsilonnµn)n is weakly bounded, is
strongly bounded, or is equicontinuous, respectively. In related work, we more than answer
the 1973 Buchwalter-Schmets question by demonstrating a Cc(X) space
that is a df-space but not a DF-space.
MARCH 11: NO SEMINAR, but three related events:
CCNY Mathematics Department Colloquium: Jerzy Kakol, Adam Mickiewicz U.
"Spaces of continuous functions over K-analytic spaces". Lunch 12:00, NAC
Faculty Dining Room; talk 1:00 NAC 4/113.
ABSTRACT:
A topological space X is said to have countable tightness if
for any subset A of X and any x in the closure of A, there exists
a countable subset of A whose closure contains x. This useful property has
been intensively studied by both analysts and topologists. Especially nice and
applicable results were obtained for spaces of continuous functions with the
topology of pointwise convergence, Cp(X). We present a short survey of this
theory with possible very new results including the case of spaces Cp(X) over
K-analytic topological spaces (X is K-analytic if it is a continuous image of
a Cech-complete Lindelof space.)
CUNY Graduate Center Computer Science, Seminar on Image Processing and
Computer Vision, 2-4pm, room 3305. Herbert Edelsbrunner, Duke University
and CUNY Graduate Student Deniz Sarioz, will discuss the use of sequences
of Betti number triples for identifying the essential nature of spatial
objects (such as biological macromolecules).
http://www.cs.gc.cuny.edu/~gherman/CSc83200.html.
CUNY Graduate Center Computer Science, Departmental Colloquium, 4:15pm,
room 9206/9207: Herbert Edelsbrunner, Duke University. "A combinatorial
algorithm based on Jacobi sets of multiple Morse functions". The abstract
is at the site:
http://web.gc.cuny.edu/Computerscience/cs_cllqm/talks/2004_03_11.html.
MARCH 18: Prabudh Misra, College of Staten Island. "Finite monothetic
subsemigroups of S(R)". At CCNY. Tea 3:15, NAC 8/133; talk 4:00 NAC
4/113. For information: R. Kopperman, rdkcc@cunyvm.cuny.edu.
ABSTRACT: The smallest closed subsemigroup \Gamma(x) containing an element x of a topological semigroup is called a
monothetic subsemigroup of the semigroup. The semigroup of all continuous selfmaps
of the reals is a topological semigroup, S(R), under the operation composition and compact-open topology. Compact monothetic subesemigroups of S(R) have been characterized by Boyce in 1971, and Magill asked in 1991 if a reasonable description of finite
monothetic subsemigroups could be given for this semigroup. In this talk we will
describe all the elements of S(R) that give finite subsemigroups.
MARCH 25: Krzysztof Jarosz, Southern Illinois U. at Edwardsville.
"Reversed Automatic Continuity Operators Determining Topology". Tea 3:15,
talk 4:00, Room 6-215 Baruch Coll. Vertical Campus, Lexington Av. and 24
St. For information contact A. Todd,
artbb@cunyvm.cuny.edu.
ABSTRACT:
Assume M(A) is a family of continuous operators on a Banach
space A. We provide partial answers to the question ``Is the
original topology of A the only complete norm topology making all the
operators from A continuous?", for multipliers and other operators. In
particular we prove that for a compact abelian group G and the circle
group T:
:· for A=Lp(T),\ 1<p<\infty, the original norm is the only one that makes all translations continuous,
:· for A=C(G),L\infty(G), L¹(G), there are other norms ith this property.
For noncompact groups the situation is different -- on L¹(R) the
L¹-norm is the only one that makes a single translation continuous.
APRIL 15: Neil Hindman, Howard University, "Almost disjoint large subsets
of semigroups". Tea 3:15, talk 4:00, Room 6-215 Baruch Coll. Vertical
Campus, Lexington Av. and 24 St. For local information contact A. Todd, artbb@cunyvm.cuny.edu.
ABSTRACT:
There are several notions of largeness in a semigroup
$(S,\cdot)$ which originated in topological dynamics and have simple
characterizations in terms of the algebraic structure of the Stone Cech
compactification $\beta S$ of $S$. These include central sets
(members of a minimal idempotent), piecewise syndetic sets (sets
whose closure meets the smallest ideal of $\beta S$), thick sets
(sets whose closure contains a left ideal of $\beta S$), and syndetic
sets (sets whose closure meets every left ideal of $\beta S$). The last
three notions also have simple elementary descriptions in terms of $S$.
The central sets are especially interesting because they are partition
regular (meaning that when a central set is divided into finitely many
pieces, one of those pieces must be central) and are guaranteed to contain
a substantial amount of combinatorial structure. We investigate the extent
to which these large sets may be split into almost disjoint families of
large sets. For example, we show that if $A$ is an alphabet with $|A|=
\kappa\geq\omega$, $S$ is the free semigroup on the alphabet $A$, there is
some almost disjoint collection of $\mu$ subsets of $A$, and $P$ is any of
the first three properties, then any subset of $S$ with property $P$ can
be split into $\mu$ almost disjoint subsets each having property $P$. On
the other hand, while any syndetic subset of $S$ can be split into
infinitely many pairwise disjoint syndetic sets, there is no collection of
$\kappaµ+$ almost disjoint syndetic subsets of $S$.
Coauthors: Tim Carlson, Jillian McLeod, and Dona Strauss.
APRIL 22: Javier Trigos California State University, Bakersfield,
"Non-measurable subgroups of compact metric abelian groups". At CSI; tea
3:15 1S/215, talk 4:00 1S/112. For parking contact P. R. Misra,
(718)982-3626, prmisra@netzero.net.
ABSTRACT:
Every group (:=infinite Abelian) has a subgroup of countable
index, therefore every compact group has a non-measurable subgroup of
countable index. In joint work with Comfort and Raczkowski, we have proven
that every compact group has
(a) a non-measurable subgroup of index as large as possible, and
(b) as many non-measurable subgroups as possible.
In this talk we focus on the case when the group is metric. Our arguments
use Bernstein's classic construction of non-measurable subsets of the real
line.
APRIL 29: Frederic Mynard, U. of Mississippi, "Coreflectively Modified
Duality". At CCNY. Tea 3:15, NAC 8/133; talk 4:00 NAC 4/113. For parking,
contact R. Kopperman, rdkcc@cunyvm.cuny.edu.
ABSTRACT:
I present a general mechanism of continuous duality together
with various applications concerning sequentiality of products of
sequential convergences, quotientness of products of quotient maps and
relations between a convergence and the upper Kuratowski convergence on
its closed sets (homeomorphically Scott convergence on the complete
lattice of its open sets). Even if one is only interested in topologies,
this is the framework of general convergences that allows development of a
unified theory.
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