Proof. There exists an open neighborhood W of xgcb such that clsWCZ U, where els W denotes the closure of W. Let [ATjfc|fe = l, 2, • • • ] be a neighborhood base at ~1 which is closed. Moreover WEW, i.e. 4>UxEW. Thus there exists k such that ATJItCWCcls W. Hence xECk. Now from WlCU...

Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F -valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uni...

A new algorithm for nding lines in images under a bounded er ror noise model is described The algorithm is based on a hier archical and adaptive subdivision of the space of line parameters but unlike previous adaptive or hierarchical line nders based on the Hough transform measures errors in image space and thereby guarantees that no solution satisfying the given error bounds will be lost In ad...

In this study, we introduce some well-known definitions and properties for multi-valued functions. We present new such as, m-retraction, m-section, m-homeomorphism, m-HEP reducible function. give a result on the relation between multi-homotopy groups m-homeomorphism. also deal with of m-HEP.

This paper concerns the link between the dynamical behaviour of a dynamical system and the dynamical behaviour of its numerical simulations. Here, we model numerical truncation as a spatial discretization of the system. Some previous works on well chosen examples (see e.g. citeGamb-dif) show that the dynamical behaviours of dynamical systems and of their discretizations can be quite different. ...

A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given. Afterwards, several applications are presented. First a global construction of monotonic and/or convex generalized splines interpolating monotonic and/or co...

Generalized maps describe the subdivision of objects in cells, and incidence and adjacency relations between cells, and they are widely used to model 2D and 3D images. Recently, we have defined submap isomorphism, which involves deciding if a copy of a pattern map may be found in a target map, and we have described a polynomial time algorithm for solving this problem when the pattern map is con...