Displaying 1101 – 1120 of 1237

Showing per page

Topological structure of the space of lower semi-continuous functions

Katsuro Sakai, Shigenori Uehara (2006)

Commentationes Mathematicae Universitatis Carolinae

Let L ( X ) be the space of all lower semi-continuous extended real-valued functions on a Hausdorff space X , where, by identifying each f with the epi-graph epi ( f ) , L ( X ) is regarded the subspace of the space Cld F * ( X × ) of all closed sets in X × with the Fell topology. Let LSC ( X ) = { f L ( X ) f ( X ) , f ( X ) ( - , ] } and LSC B ( X ) = { f L ( X ) f ( X ) is a bounded subset of } . We show that L ( X ) is homeomorphic to the Hilbert cube Q = [ - 1 , 1 ] if and only if X is second countable, locally compact and infinite. In this case, it is proved that ( L ( X ) , LSC ( X ) , LSC B ( X ) ) is homeomorphic to ( Cone Q , Q × ( 0 , 1 ) , Σ × ( 0 , 1 ) ) (resp. ( Q , s , Σ ) ) if X is compact (resp. X is non-compact), where Cone Q = ( Q × 𝐈 ) / ( Q × { 1 } ) is the cone over...

Topologically invariant σ-ideals on Euclidean spaces

T. Banakh, M. Morayne, R. Rałowski, Sz. Żeberski (2015)

Fundamenta Mathematicae

We study and classify topologically invariant σ-ideals with an analytic base on Euclidean spaces, and evaluate the cardinal characteristics of such ideals.

Traces, lengths, axes and commensurability

Alan W. Reid (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.

Trees of manifolds with boundary

Paweł Zawiślak (2015)

Colloquium Mathematicae

We introduce two new classes of compacta, called trees of manifolds with boundary and boundary trees of manifolds with boundary. We establish their basic properties.

Tritangent planes to toroidal knots.

A. Montesinos Amilibia (1991)

Revista Matemática de la Universidad Complutense de Madrid

A proof is given that, with the only exception of (3,2), all toroidal knots in R3 obtained in the standard way by stereographic projection of knots in S3 have tritangent planes.

Currently displaying 1101 – 1120 of 1237