147,162 research outputs found
Relation proximal point with some dynamical properties
In this paper we discussed relation proximal points with many of dynamical properties through studied topological transformation group , and it will given necessary condition for proximal relation to be minimal set ,and introduce new define replete set and semi-replete set by using concept of the replete set and semi-replete set as well as we introduce that many of new relations and theorem. Key words: Proximal point, replete proximal point, syndetic set, semi-replete set, minimal set, almost periodic point            .
Applications of pre-open sets
[EN] Using the concept of pre-open set, we introduce and study topological properties of pre-limit points, pre-derived sets, preinterior and pre-closure of a set, pre-interior points, pre-border, prefrontier and pre-exterior. The relations between pre-derived set (resp. pre-limit point, pre-interior (point), pre-border, pre-frontier, and preexterior) and α-derived set (resp. α-limit point, α-interior (point), α-border,
α-frontier, and α-exterior) are investigatedJun, YB.; Jeong, SW.; Lee, HJ.; Lee, JW. (2008). Applications of pre-open sets. Applied General Topology. 9(2):213-228. https://doi.org/10.4995/agt.2008.18022132289
Road Systems and Betweenness
A road system is a collection of subsets of a set—the roads—such that every singleton subset is a road in the system and every doubleton subset is contained in a road. The induced ternary (betweenness) relation is defined by saying that a point c lies between points a and b if c is an element of every road that contains both a and b . Traditionally, betweenness relations have arisen from a plethora of other structures on a given set, reflecting intuitions that range from the order-theoretic to the geometric and topological. In this paper we initiate a study of road systems as a simple mechanism by means of which a large majority of the classical interpretations of betweenness are induced in a uniform way
Topological Ramsey spaces from Fra\"iss\'e classes, Ramsey-classification theorems, and initial structures in the Tukey types of p-points
A general method for constructing a new class of topological Ramsey spaces is
presented. Members of such spaces are infinite sequences of products of
Fra\"iss\'e classes of finite relational structures satisfying the Ramsey
property. The Product Ramsey Theorem of Soki\v{c} is extended to equivalence
relations for finite products of structures from Fra\"iss\'e classes of finite
relational structures satisfying the Ramsey property and the Order-Prescribed
Free Amalgamation Property. This is essential to proving Ramsey-classification
theorems for equivalence relations on fronts, generalizing the Pudl\'ak-R\"odl
Theorem to this class of topological Ramsey spaces.
To each topological Ramsey space in this framework corresponds an associated
ultrafilter satisfying some weak partition property. By using the correct
Fra\"iss\'e classes, we construct topological Ramsey spaces which are dense in
the partial orders of Baumgartner and Taylor in \cite{Baumgartner/Taylor78}
generating p-points which are -arrow but not -arrow, and in a partial
order of Blass in \cite{Blass73} producing a diamond shape in the Rudin-Keisler
structure of p-points. Any space in our framework in which blocks are products
of many structures produces ultrafilters with initial Tukey structure
exactly the Boolean algebra . If the number of Fra\"iss\'e
classes on each block grows without bound, then the Tukey types of the p-points
below the space's associated ultrafilter have the structure exactly
. In contrast, the set of isomorphism types of any product
of finitely many Fra\"iss\'e classes of finite relational structures satisfying
the Ramsey property and the OPFAP, partially ordered by embedding, is realized
as the initial Rudin-Keisler structure of some p-point generated by a space
constructed from our template.Comment: 35 pages. Abstract and introduction re-written to make very clear the
main points of the paper. Some typos and a few minor errors have been fixe
Critical manifolds and stability in Hamiltonian systems with non-holonomic constraints
We explore a particular approach to the analysis of dynamical and geometrical
properties of autonomous, Pfaffian non-holonomic systems in classical
mechanics. The method is based on the construction of a certain auxiliary
constrained Hamiltonian system, which comprises the non-holonomic mechanical
system as a dynamical subsystem on an invariant manifold. The embedding system
possesses a completely natural structure in the context of symplectic geometry,
and using it in order to understand properties of the subsystem has compelling
advantages. We discuss generic geometric and topological properties of the
critical sets of both embedding and physical system, using Conley-Zehnder
theory and by relating the Morse-Witten complexes of the 'free' and constrained
system to one another. Furthermore, we give a qualitative discussion of the
stability of motion in the vicinity of the critical set. We point out key
relations to sub-Riemannian geometry, and a potential computational
application.Comment: LaTeX, 52 pages. Sections 2 and 3 improved, Section 5 adde
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