Search results for "Geometry and Topology"
showing 10 items of 457 documents
On t-covers in finite projective spaces
1979
A t-cover of the finite projective space PG(d,q) is a setS of t-dimensional subspaces such that any point of PG(d,q) is contained in at least one element ofS. In Theorem 1 a lower bound for the cardinality of a t-coverS in PG(d,q) is obtained and in Theorem 2 it is shown that this bound is best possible for all positive integers t,d and for any prime-power q.
Mixed intersections of non quasi-analytic classes
2008
Given two semi-regular matrices M and M' and two open subsets O and O' [resp. two compact subsets K and K'] of Rr and Rs respectively, we introduce the spaces E(M×M')(O × O') and D(M×M')(O × O') [resp. D(M×M')(K × K')]. In this paper we study their locally convex properties and the structure of their elements. This leads in [10] to tensor product representations of these spaces and to some kernel theorems.
Convergence-theoretic characterizations of compactness
2002
AbstractFundamental variants of compactness are characterized in terms of concretely reflective convergence subcategories: topologies, pretopologies, paratopologies, hypotopologies and pseudotopologies. Hyperquotient maps (perfect, quasi-perfect, adherent and closed) and quotient maps (quotient, hereditarily quotient, countably biquotient, biquotient, and almost open) are characterized in terms of various degrees of compactness of their fiber relations, and of sundry relaxations of inverse continuity.
Topological invariants of stable immersions of oriented 3-manifolds in R4
2012
Abstract We show that the Z -module of first order local Vassiliev type invariants of stable immersions of oriented 3-manifolds into R 4 is generated by 3 topological invariants: The number of pairs of quadruple points and the positive and negative linking invariants l + and l − introduced by V. Goryunov (1997) [7] . We obtain the expression for the Euler characteristic of the immersed 3-manifold in terms of these invariants. We also prove that the total number of connected components of the triple points curve is a non-local Vassiliev type invariant.
Introduction to generalized topological spaces
2011
[EN] We introduce the notion of generalized topological space (gt-space). Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants) in terms of generalized spaces.
The terminal hyperspace of homogeneous continua
2010
Abstract We investigate the structure of the collection of terminal subcontinua in homogeneous continua. The main result is a reduction of this structure to six specific types. Three of these types are of one-dimensional spaces, and examples representing these types are known. It is not known whether higher dimensional examples having non-trivial terminal subcontinua and representing the three remaining types exist.
Strongly invertible links and divides
2008
Abstract To a proper generic immersion of a finite number of copies of the unit interval in a 2-disc, called a divide, A’Campo associates a link in S 3 . From the more general notion of ordered Morse signed divides, one obtains a braid presentation of links of divides. In this paper, we prove that every strongly invertible link is isotopic to the link of an ordered Morse signed divide. We give fundamental moves for ordered Morse signed divides and show that strongly invertible links are equivalent if and only if we can pass from one ordered Morse signed divide to the other by a sequence of such moves. Then we associate a polynomial to an ordered Morse signed divide, invariant for these move…
Classical sequences revisited with permutations avoiding dotted pattern
2011
International audience; Inspired by the definition of the barred pattern-avoiding permutation, we introduce the new concept of dotted pattern for permutations. We investigate permutations classes avoiding dotted patterns of length at most 3, possibly along with other classical patterns. We deduce some enumerating results which allow us to exhibit new families of permutations counted by the classical sequences: 2^n, Catalan, Motzkin, Pell, Fibonacci, Fine, Riordan, Padovan, Eulerian.
Fuzzy functions: a fuzzy extension of the category SET and some related categories
2000
<p>In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -&gt; L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.</p>
A common fixed point theorem for two weakly compatible pairs in G-metric spaces using the property E.A
2013
In view of the fact that the fixed point theory provides an efficient tool in many fields of pure and applied sciences, we use the notion of the property E.A to prove a common fixed point theorem for weakly compatible mappings. The presented results are applied to obtain the solution of an integral equation and the bounded solution of a functional equation arising in dynamic programming.