Induced Hausdorff Metrics on Quotient Spaces

Metrics of positive Ricci curvature on quotient spaces

One of the classical problems in differential geometry is the investigation of closed manifolds which admit Riemannian metrics with given lower bounds for the sectional or the Ricci curvature and the study of relations between the existence of such metrics and the topology and geometry of the underlying manifold. Despite many efforts during the past decades, this problem is still far from being...

On soft Hausdorff spaces

The aim of this paper is to study some properties of soft Hausdorff space introduced by Shabir and Naz. Firstly, we give a representation of soft sets and soft topological spaces. Secondly, we introduce some new concepts in soft topological space such as convergence of sequences, homeomorphism and investigate the relations between these concepts and Hausdorff axiom in soft topological space. 20...

Norms on Quotient Spaces

Biased Estimators on Quotient Spaces

Usual statistics are defined, studied and implemented on Euclidean spaces. But what about statistics on other mathematical spaces, like manifolds with additional properties: Lie groups, Quotient spaces, Stratified spaces etc? How can we describe the interaction between statistics and geometry? The structure of Quotient space in particular is widely used to model data, for example every time one...

On Hausdorff-like metrics for fuzzy sets

In (Chaudhuri and Rosenfeld, 1996), metrics were developed for fuzzy sets u and v defined on the same support set S. These metrics are based on applying the Hausdorff metric to pairs of membership level sets (u 1 ( [ tk, 1 ] ), v1 ( [ tk, 1 ] ) ), where tk E [0, 1] is a (possible) membership value of u or v. The metrics of (Chaudhuri and Rosenfeld, 1996) give nice comparisons of fuzzy sets by m...