Introduction. In this note we study the topological and metric structure of conformal repellor X C K, m > 1, of topological dimension 1. The definition of conformal repellor is given in the next two sections. We then show the following dichotomy: either the Hausdorff dimension of X exceeds 1 or else X is a Jordan curve (simple closed curve) and its 1-dimensional Hausdorff measure is positive an...

We propose a new approach to assigning distance between fuzzy numbers. A pseudo-metric on the set of fuzzy numbers and a metric on the set of trapezoidal fuzzy numbers are described. The regular reducing functions and the Hausdorff metric are used to define the metric. Using this metric, we can approximate an arbitrary generalized left right fuzzy number with a trapezoidal one. Finally, powers ...

We equip the space M(X) of all Borel probability measures an a compact Riemannian manifold X with a canonical distance function which induces the weak-∗ topology on M(X) and has the following property: the map X 7→ M(X) is Lipschitz continous with respect to the Gromov-Hausdorff distance on the space of all the (isometry classes of) compact metric spaces. Introduction Last century brought sever...

It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodi...

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

We study the structure of strictly singular non-compact operators between $L\_p$ spaces. Answering a question raised in earlier work on interpolation properties operators, it is shown that there exist $T$, for which set points $(1/p,1/q)\in(0,1)\times (0,1)$ such $T\colon L\_p\rightarrow L\_q$ but not compact contains line segment triangle ${(1/p,1/q):1\<p\<q<\infty}$ any positive slope. This w...

In this paper we introduce a new notion of generalized metric, called i-metric. This generalization is made by changing the valuation space of the distance function. The result is an interesting distance function for the set of fuzzy numbers of Interval Type with non negative fuzzy numbers as values. This example of i-metric generates a topology in a very natural way, based on open balls. We pr...

Intrinsic Lp metrics are defined and shown to satisfy a dimension–free bound with respect to the Hausdorff metric. MSC 2000: 52A20, 52A27, 52A40, 60G15.

This lecture describes the holonomy group for a 4-dimensional Hausdorff, connected and simply connected manifold admitting a Lorentz metric and shows, briefly, some applications to Einstein’s space-time of general relativity. 1. Holonomy Theory on 4-Dimensional Lorentz Manifolds. Let M be a 4-dimensional, smooth, Hausdorff, connected, and simply connected manifold admitting a smooth Lorentz met...

We use geometric properties of Gromov-Hausdorff-convergence to present a way to construct rough but natural invariants of metric geometry.