NORMAL MAPS AND HYPERBOLICITY

×ØÖ Øº Criteria for a complex space to be hyperbolic, hyperbolically imbedded, taut or tautly imbedded are presented. In particular, the following generalization of theorems by Eastwood and Kobayashi is produced by replacing the requirement of hyperbolicity of the image space by normality of the mapping: Let f : X → Z be a normal map between complex spaces X and Z. If eithe

Compactness via Adherence Dominators

This talk is based on a joint work by T. A. Edwards, J. E. Joseph, M. H. Kwack and B. M. P. Nayar that apperared in the Journal of Advanced studies in Topology, Vol. 5 (4), 2014), 8 - 15. B An adherence dominator on a topological space X is a function π from the collection of filterbases on X to the family of closed subsets of X satisfying A(Ω) ⊆ π(Ω) where A(Ω) is the adherence of Ω. The notations π(Ω) and A(Ω) are used for the values of the functions π and A and π(Ω) =⋂_Ω π F= ⋂_O π V, where O represents the open members of Ω. The π -adherence may be adherence,θ- adherence, u-adherence s-adherence,f- adherence δ-adherence etc., of a filterbase. Many of the recent theorems by the authors and others on Hausdorff-closed, Urysohn-closed, and regular-closed spaces are subsumed in this paper. It is also shown that a space X is compact if and only if for each upper-semi-continuous relation β on X with π -strongly closed graph, the relation μ on X defined by μ = πβ has a maximal value with respect to set inclusion