Displaying similar documents to “The second Yamabe invariant with singularities”

Kuratowski convergence on compacta and Hausdorff metric convergence on compacta

Primo Brandi, Rita Ceppitelli, Ľubica Holá (1999)

Commentationes Mathematicae Universitatis Carolinae

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This paper completes and improves results of [10]. Let ( X , d X ) , ( Y , d Y ) be two metric spaces and G be the space of all Y -valued continuous functions whose domain is a closed subset of X . If X is a locally compact metric space, then the Kuratowski convergence τ K and the Kuratowski convergence on compacta τ K c coincide on G . Thus if X and Y are boundedly compact metric spaces we have the equivalence of the convergence in the Attouch-Wets topology τ A W (generated by the box metric of d X and d Y ) and τ K c convergence...

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let D be a nonempty compact subset of a Banach space X and denote by S ( X ) the family of all nonempty bounded closed convex subsets of X . We endow S ( X ) with the Hausdorff metric and show that there exists a set ℱ ⊂ S ( X ) such that its complement S ( X ) ∖ ℱ is σ -porous and such that for each A ∈ ℱ and each x ˜ ∈ D , the set of solutions of the best approximation problem ∥ x ˜ - z ∥ → min , z ∈ A , is nonempty and compact, and each minimizing sequence has a convergent subsequence.