NEW YORK SEMINAR ON GENERAL TOPOLOGY AND TOPOLOGICAL ALGEBRA
February - June 2008
CHECK FOR CAMPUS AND LOCATION
FEBRUARY 21: Prabudh Misra, College of Staten Island, CUNY,
will discuss "Principal Ideals of S(R)". At Baruch College Vertical Campus, Lexington
Avenue and 24th Street. Tea 3:15 p.m., talk 4:00 p.m., Mathematics Conference Room, 6-215.
For more information, contact A. Todd, artodd@panix.com.
ABSTRACT: The left and right principal
ideals of the semigroup of continuous selfmaps of the reals ( S(R) ) are algebraically
different objects. Using some general theorems proved by Ken Magill and myself, we will
establish the relationship between the generators of two isomorphic left principal ideals.
Analogous results for the right principal ideals will also be given. The corresponding theorems
for the near-ring of continuous selfmaps of the reals will be presented as well.
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MARCH 13: John S. Antrobus, CCNY and CUNY Graduate Center Department
of Psychology, "Context Enhances Recognition Utility by Biasing the Recognition Process:
Recognizing Degraded Words Is Not a Random Walk", at CCNY. Tea 3pm, NAC 8/133, talk 4pm,
NAC 6307. For more Information, parking: R. Kopperman,
rdkcc@ccny.cuny.edu.
ABSTRACT: [Joint work with: Yusuke Shono,
Martin Duff, Reza Farahani (CUNY Graduate Center, Psychology), and Bala Sundaram (U. Mass.
Boston)]. Fast accurate reading is facilitated by context-appropriate biases that optimize
recognition speed and accuracy by reducing the amount of target information required for
accurate recognition. Recognition terminates when improved accuracy no longer offsets
recognition cost. In the reverse Target-Forced-choice (FC) recognition task (target mask
FC words), both FC words and repetition primes bias the recognition of degraded partially-
recognized, masked targets. Comparison of accuracy, confidence, and response times to Left
and Right FC cues shows that repetition priming biases recognition of the FC cues. Both
cues and primes, in turn, increase target accuracy by biasing the sensitivity of the FC
attractors. These biases extend to representations of target letters but not to letter
features, so that priming bias occurs only when FC cues are similar (have several common
letters). These findings are incompatible with the drift diffusion model but strongly support
its recognition bias assumption.
This paper addresses the representation of visual word form
recognition, how recognition is biased when constrained by contextual information, how when
context is appropriate, this bias facilitates, accelerates or enhances accuracy. It
proposes that the criterion for terminating the recognition process the point where the
estimate of further gain/benefit (i.e. accuracy) is no longer offset by the cost (time) of
continued processing. Unlike the Drift Diffusion model based on the Random Walk model which
assumes that the criterion is determined prior to trial onset, our Fast Accurate Recognition
in Context (RARIC) model assumes that the criterion is determined within the recognition
interval. FARIC is a three-layered attractor model. Recognition of both target and FC words
is the activation of successive actions in the multi-layered word system, where each layer
is an attractor landscape of interacting multidimensional vectors, each of which has recurrent
connections with the vectors in adjacent landscapes. (Note, in order to represent the
non-linear relations between adjacent layers, there is a hidden layer between each of the
3 landscapes.)
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MARCH 20: Francis Jordan, Georgia Southern U., "Coincidence of topologies
on function spaces", at CCNY. Tea 3pm, NAC 8/133, talk 4pm NAC 6307. For more Information,
parking: R. Kopperman, rdkcc@ccny.cuny.edu .
ABSTRACT: We consider the compact-open,
Isbell, and finest splitting topologies on the set of [X,R] of continuous real valued functions
with completely regular domain X and codomain the real numbers. Generally, the compact-open,
Isbell, and finest splitting topologies are of increasing fineness.
Conditions on X are considered that will make some of these
topologies the same. It is well known that the topologies are all the same if X is locally
compact. We will show that the converse implication is true for many common spaces such as
metric spaces. In fact we will show that for such space, if the Isbell and finest splitting
topologies are the same, then X is locally compact. These results arise from a consideration
of a topology on the set of upper semi continuous relations on the product of X and R.
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APRIL 10: Robert Page, Framingham State College, "Triadjoints of
bounded bilinear operations". At C.W. Post; Tea 3:15, Pell Hall 240; talk at 4:00 Pell Hall, 242.
For more information, call C.W. Post Math Department at 516-299-2448 or write
SAndima@liu.edu.
ABSTRACT: Let X,Y,Z be normed linear spaces
and m:XxY->Z be a norm bounded bilinear operation. In 1951, Arens introduced the adjoint of m,
denoted by m*:Z'xX->Y', where for all f in Z', x in X, y in Y, m*(f,x)(y)=f(m(x,y)).
The triadjoint of m is, in almost every conceivable sense, an
extension of m. In fact, if X=Y=Z and m is an associative multiplication then m*** also is
an associative multiplication on X". The triadjoint of a commutative map may fail to be
commutative, however. In case X=Y, define m', the transpose of m, by m'(x,y)=m(y,x) for
every x,y in X. The bilinear map m is called Arens regular if m'***'=m***. In his paper,
Arens gave an example of a positive bilinear map on l_1xl_1 that is not Arens regular.
We will put Arens' counterexample in the proper context, that is, we will show that the
existence of non-regular maps is characterized by the presence of l_1.
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MAY 8: Yung Kong, Queens College, "A Method of Verifying the
Topological Soundness of Parallel Thinning Algorithms for 2D, 3D, and 4D Binary Images,"
Joint with Computer Science Colloquium. Talk 4:15-5:30, CUNY Graduate Center, 9206/9207;
followed wine and cheese reception, 4102.
ABSTRACT: A finite set D of 1s of a binary
image is "deletable" if the union of the 1s of the image can be continuously deformed over
itself onto the union of the 1s that are not in D (i.e., the latter union is a deformation
retract of the former union). D is "codeletable" if the union of the elements of D and all
the 0s of the image can be continuously deformed over itself onto the union of just
the 0s of the image.
Parallel thinning algorithms are iterative algorithms used to
reduce objects in binary images to thin skeletons. Each iteration changes certain 1s of the
image to 0s. There are two main types of thinning algorithm: those for which the set of 1s
deleted at each iteration is a deletable set, and those for which the set of 1s deleted at
each iteration is a codeletable set. It is generally non-trivial to prove that a proposed
thinning algorithm satisfies either of these "topology preservation" conditions. On the
2-d Cartesian grid, a systematic and powerful proof method was introduced by Ronse in the
1980s, based on two results:
(1) a finite set D of 1s and its proper subsets are all
codeletable if each singleton and each pair of 8-adjacent pixels in D is
codeletable, and
(2) D and its proper subsets are all deletable if
(a) each singleton and each pair
of 4-adjacent pixels in D is deletable, and
(b) no set of 2, 3, or 4 pairwise
8-adjacent pixels that is an 8-connected component of the 1s of the image is entirely
contained in D.
Analogous results were obtained by Hall, Ma, Gau, and the author
for binary images on the 2-d hexagonal grid, the 3-d Cartesian and face-centered-cubic grids,
and the 4-d Cartesian grid. This allowed Ronse's method to be extended to those four grids.
This work has been unified and generalized to almost any polytopal complex whose union is
2-, 3-, or 4-dimensional Euclidean space.
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MAY 29: Frederic Mynard, Georgia Southern University, "Stability of local
topological properties under product", at Queens College. Tea 3:30 in Kiely 508, talk 4:30
in Kiely 242. For local information and parking, contact G. Itzkowitz,
718-997-5849, gitzkowitz@prodigy.net.
ABSTRACT: Many important local topological
properties such as, for instance, the Frechet-Urysohn property, tightness, and fan-tightness
fail to be stable under product, or even under the operation of taking the supremum of two
topologies on the same set. In each case, sufficient conditions on the factor spaces to ensure
that the product space has the desired property have been the focus of extensive work (by
A. Arhangelskii, A. Bella, E. Michael, T. Nogura, J. Van Mill, to cite only a few).
After an introduction about relevant examples of topological
properties to be considered, I will present an abstract scheme using relations on filters that
leads to unifying results concerning the problem of stability under product. Corollaries
recover or refine a large number of classical and of recent results in the area, and also
include entirely new results. An interesting feature of the approach is that the abstract
results could find other applications beyond those given as illustrative examples.
This is joint work with Francis Jordan.
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JUNE 12: Vladimir Tkachuk, U. Autonoma Metropolitana, Mexico City,
"A selection principle for dense subsets", at City College. Tea 3:15 in NAC 8/134, talk 4:00
in NAC 5/148. For local information and parking, contact R. Kopperman, rdkcc@ccny.cuny.edu.
ABSTRACT: This is a joint work with A. Bella,
M. Bonanzinga, and M. Matveev. A space X is called selectively separable if, for any
sequence \{Dn:n\in \omega\} of dense subsets of X we can choose, for
every n\in \omega, a finite set An\subset Dn in such a way
that \bigcup\{An:n\in \omega\} is dense in X. It is not difficult to
see that every space of countable \pi-weight is selectively separable while even
countable spaces can fail to be selectively separable. We study this notion for general
spaces with an essential emphasis on countable ones. In particular, we show that it is
independent of ZFC whether every dense countable subspace of \{0,1\}^{\omega1}
is selectively separable; we characterize selective separability in Cp(X)
and show that it is consistent with ZFC that there exists a regular maximal countable space
which is not selectively separable.
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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
Medgar Evers
(718-270-6125): H. Pajoohesh