Bi-quotient maps and cartesian products of quotient maps

Relative Compactness and Product Stable Quotient Maps

relative compactness and product stable quotient maps

Generalized tri-quotient maps and Čech-completeness

For a topological space X let K(X) be the set of all compact subsets of X. The purpose of this paper is to characterize Lindelöf Čech-complete spaces X by means of the sets K(X). Similar characterizations also hold for Lindelöf locally compact X, as well as for countably K-determined spaces X. Our results extend a classical result of J. Christensen.

Asymptotic Geometry of Banach Spaces and Uniform Quotient Maps

Recently, Lima and Randrianarivony pointed out the role of the property (β) of Rolewicz in nonlinear quotient problems, and answered a ten-year-old question of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. In the present paper, we prove that the modulus of asymptotic uniform smoothness of the range space of a uniform quotient map can be compared with the modulus of (β) of the domain spa...

Quotient Maps with Connected Fibers and the Fundamental Group

In classical covering space theory, a covering map induces an injection of fundamental groups. This note reveals a dual property for quotient maps having connected fibers, with applications to orbit spaces of smooth vector fields and leaf spaces in general.