University of Nebraska-Lincoln
DePauw University
Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis,
2017
Cylance, Inc.
Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
Conference Program,
2017
University of Dayton
Conference Program, University Of Dayton
Summer Conference on Topology and Its Applications
Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications.
Pseudo-Contractibility,
2017
Universidad Autonoma del Estado de Mexico
Pseudo-Contractibility, Felix Capulín, Leonardo Juarez-Villa, Fernando Orozco
Summer Conference on Topology and Its Applications
Let X, Y be topological spaces and let f, g:X→ Y be mappings, we say that f is pseudo-homotopic to g if there exist a continuum C, points a, b ∈ C and a mapping H:X ×C → Y such that H(x, a)=f(x) and H(x, b)=g(x) for each x ∈ X. The mapping H is called a pseudo-homotopy between f and g. A topological space X is said to be pseudo-contractible if the identity mapping is pseudo-homotopic to a constant mapping in X. i.e., if there exist a continuum C, points a, b ∈ C ...
On A Construction Of Some Class Of Metric Spaces,
2017
Adam Mickiewicz University of Poznan
On A Construction Of Some Class Of Metric Spaces, Dariusz Bugajewski
Summer Conference on Topology and Its Applications
In this talk we are going to describe Sz´az’s construction of some class of metric spaces. Most of all we will analyze topological properties of metric spaces obtained by using Sz´az’s construction. In particular, we provide necessary and sufficient conditions for completeness of metric spaces obtained in this way. Moreover, we will discuss the relation between Sz´az’s construction and the “linking construction”. A particular attention will be drawn to the “floor” metric, the analysis of which provides some interesting observations.
Disjoint Infinity Borel Functions,
2017
University of Denver
Disjoint Infinity Borel Functions, Daniel Hathaway
Summer Conference on Topology and Its Applications
Consider the statement that every uncountable set of reals can be surjected onto R by a Borel function. This is implied by the statement that every uncountable set of reals has a perfect subset. It is also implied by a new statement D which we will discuss: for each real a there is a Borel function fa : RtoR and for each function g : RtoR there is a countable set G(g) of reals such that the following is true: for each a in R and for each function g : R to R, if fa is disjoint from g ...
On Di-Injective T0-Quasi-Metric Spaces,
2017
North-West University (South Africa)
On Di-Injective T0-Quasi-Metric Spaces, Collins Amburo Agyingi
Summer Conference on Topology and Its Applications
We prove that every q-hyperconvex T0-quasi-metric space (X, d) is di-injective without appealing to Zorn’s lemma. We also demonstrate that QX as constructed by Kemajou et al. and Q(X) (the space of all Katˇetov function pairs on X) are di-injective. Moreover we prove that di-injective T0-quasi-metric spaces do not contain proper essential extensions. Among other results, we state a number of ways in which the the di-injective envelope of a T0-quasi-metric space can be characterized.
Some New Completeness Properties In Topological Spaces,
2017
Gazi University
Some New Completeness Properties In Topological Spaces, Cetin Vural, Süleyman Önal
Summer Conference on Topology and Its Applications
One of the most widely known completeness property is the completeness of metric spaces and the other one being of a topological space in the sense of Cech. It is well known that a metrizable space X is completely metrizable if and only if X is Cech-complete. One of the generalisations of completeness of metric spaces is subcompactness. It has been established that, for metrizable spaces, subcompactness is equivalent to Cech-completeness. Also the concept of domain representability can be considered as a completeness property. In [1], Bennett and Lutzer proved that Cech-complete spaces are domain representable. They also proved, in ...
A New Class Of Dendrites Having Unique Second Symmetric Product,
2017
Universidad Autonoma del Estado de Mexico
A New Class Of Dendrites Having Unique Second Symmetric Product, David Maya, José G. Anaya, Fernando Orozco Zitli
Summer Conference on Topology and Its Applications
The second symmetric product of a continuum X, F2(X), is the hyperspace consisting of all nonempty subsets of X having at most two points. A continuum X has unique hyperspace F2(X) provided that each continuum Y satisfying that F2(X) and F2(Y) are homeomorphic must be homeomorphic to X. In this talk, a new class of dendrites having unique F2(X) will be presented.
Compactness Via Adherence Dominators,
2017
Morgan State University
Compactness Via Adherence Dominators, Bhamini M. P. Nayar, Terrence A. Edwards, James E. Joseph, Myung H. Kwack
Summer Conference on Topology and Its Applications
This talk is based on a joint work by T. A. Edwards, J. E. Joseph, M. H. Kwack and B. M. P. Nayar that apperared in the Journal of Advanced studies in Topology, Vol. 5 (4), 2014), 8 - 15. B
An adherence dominator on a topological space X is a function π from the collection of filterbases on X to the family of closed subsets of X satisfying A(Ω) ⊆ π(Ω) where A(Ω) is the adherence of Ω. The notations π(Ω) and A(Ω) are used for the values of the functions π and A and π ...
Revelation Of Nano Topology In Cech Rough Closure Spaces,
2017
Madurai Kamaraj University
Revelation Of Nano Topology In Cech Rough Closure Spaces, V. Antonysamy, Llellis Thivagar, Arockia Dasan
Summer Conference on Topology and Its Applications
The concept of Cech closure space was initiated and developed by E. Cech in 1966. Henceforth many more research scholars set their minds in this theory and developed it to a new height. Pawlak.Z derived and gave shape to Rough set theory in terms of approximation using equivalence relation known as indiscernibility relation. Further Lellis Thivagar enhanced rough set theory into a topology, called Nano Topology, which has at most five elements in it and he also extended this into multi granular nano topology. The purpose of this paper is to derive Nano topology in terms of Cech rough ...
Entropy In Topological Groups, Part 2,
2017
University of Udine
Entropy In Topological Groups, Part 2, Dikran Dikranjan
Summer Conference on Topology and Its Applications
Entropy was introduced first in thermodynamics and statistical mechanics, as well as information theory. In the last sixty years entropy made its way also in topology, ergodic theory, as well as other branches of mathematics as algebra, geometry and number theory where dynamical systems appear in one way or another.
Roughly speaking, entropy is a non-negative real number or infinity assigned to a "selfmap" T of a "space" X, where the "space" X can be a topological or uniform space, a measure space, an abstract or topological group (or vector space) or just a set. The "selfmap" T can be ...
Cohen Reals And The Sequential Order Of Groups,
2017
Tennessee Technological University
Cohen Reals And The Sequential Order Of Groups, Alexander Shibakov
Summer Conference on Topology and Its Applications
We show that adding uncountably many Cohen reals to a model of diamond results in a model with no countable sequential group with an intermediate sequential order. The same model has an uncountable group of sequential order 2. We also discuss related questions.
On The Chogoshvili Homology Theory Of Continuous Maps Of Compact Spaces,
2017
Batumi Shota Rustaveli State University
On The Chogoshvili Homology Theory Of Continuous Maps Of Compact Spaces, Anzor Beridze, Vladimer Baladze
Summer Conference on Topology and Its Applications
In this paper an exact homology functor from the category MorC of continuous maps of compact Hausdorff spaces to the category LES of long exact sequences of abelian groups is defined (cf. [2], [3], [5]). This functor is an extension of the Hu homology theory, which is uniquely defined on the category of continuous maps of finite CW complexes and is constructed without the relative homology groups [9]. To define the given homology functor we use the Chogoshvili construction of projective homology theory [7], [8]. For each continuous map f:X → Y of compact spaces, using the notion of ...
Sequential Order Of Compact Scattered Spaces,
2017
University of North Carolina at Charlotte
Sequential Order Of Compact Scattered Spaces, Alan Dow
Summer Conference on Topology and Its Applications
A space is sequential if the closure of set can be obtained by iteratively adding limits of converging sequences. The sequential order of a space is a measure of how many iterations are required. A space is scattered if every non-empty set has a relative isolated point. It is not known if it is consistent that there is a countable (or finite) upper bound on the sequential order of a compact sequential space. We consider the properties of compact scattered spaces with infinite sequential order.
Entropy Of Induced Continuum Dendrite Homeomorphisms,
2017
Universidade Federal do Rio de Janeiro
Entropy Of Induced Continuum Dendrite Homeomorphisms, Jennyffer Bohorquez, Alexander Arbieto
Summer Conference on Topology and Its Applications
Let f: D → D be a dendrite homeomorphism. Let C(D) denote the hyperspace of all nonempty connected compact subsets of D endowed with the Hausdorff metric. Let C(f):C(D) → C(D) be the induced continuum homeomorphism. In this talk we sketch the proof of the following result: If there exists a nonrecurrent branch point then the topological entropy of C(f) is ∞.
A Trace Formula For Foliated Flows (Working Paper),
2017
Universidade de Santiago de Compostela
A Trace Formula For Foliated Flows (Working Paper), Jesús A. Álvarez López, Yuri A. Kordyukov, Eric Leichtnam
Summer Conference on Topology and Its Applications
The talk, based on work in progress, will be about our progress to show a trace formula for foliated flows on foliated spaces, which has been conjectured by V. Guillemin, and later by C. Deninger with more generality. It describes certain Leftchetz distribution of the foliated flow, acting on some version of the leafwise cohomology, in terms of local data at the closed orbits and fixed points.
The Specification Property And Infinite Entropy For Certain Classes Of Linear Operators,
2017
Christopher Newport University
The Specification Property And Infinite Entropy For Certain Classes Of Linear Operators, James Kelly, Will Brian, Tim Tennant
Summer Conference on Topology and Its Applications
We study the specification property and infinite topological entropy for two specific types of linear operators: translation operators on weighted Lebesgue function spaces and weighted backward shift operators on sequence F-spaces.
It is known from the work of Bartoll, Martinínez-Giménez, Murillo-Arcila (2014), and Peris, that for weighted backward shift operators, the existence of a single non-trivial periodic point is sufficient for specification. We show this also holds for translation operators on weighted Lebesgue function spaces. This implies, in particular, that for these operators, the specification property is equivalent to Devaney chaos. We also show that these forms of chaos imply ...
Uncountably Many Quasi-Isometry Classes Of Groups Of Type Fp,
2017
University of Oklahoma
Uncountably Many Quasi-Isometry Classes Of Groups Of Type Fp, Ignat Soroko, Robert Kropholler, Ian Leary
Summer Conference on Topology and Its Applications
An interplay between algebra and topology goes in many ways. Given a space X, we can study its homology and homotopy groups. In the other direction, given a group G, we can form its Eilenberg-Maclane space K(G, 1). It is natural to wish that it is `small' in some sense. If K(G, 1) space has n-skeleton with finitely many cells, then G is said to have type Fn. Such groups act naturally on the cellular chain complex of the universal cover for K(G, 1), which has finitely generated free modules in all dimensions up to n ...
On Roitman's Principle For Box Products,
2017
Universidad Nacional Autonoma de Mexico
On Roitman's Principle For Box Products, Hector Alonso Barriga-Acosta
Summer Conference on Topology and Its Applications
One of the oldest problems in box products is if the countable box product of the convergent sequence is normal. It is known that consistenly (e.g., b=d, d=c) the answer is affirmative. A recent progress is due to Judy Roitman that states a combinatorial principle which also implies the normality and holds in many models.
Although the countable box product of the convergent sequence is normal in some models of b < d < c, Roitman asked what happen with her principle in this models. We answer that Roitman's principle is true in some models of b < d < c.
On Quasi-Uniform Box Products,
2017
North-West University (South Africa)
On Quasi-Uniform Box Products, Hope Sabao, Olivier Olela Otafudu
Summer Conference on Topology and Its Applications
In this talk, we preset the quasi-uniform box product, a topology that is finer than the Tychonov product topology but coarser than the uniform box product.
We then present various notions of completeness of a quasi-uniform space that are preserved by their quasi-uniform box product using Cauchy filter pairs.
