Intrinsic flat convergence of covering spaces

Flat Convergence for Integral Currents in Metric Spaces

It is well known that in compact local Lipschitz neighborhood retracts in Rn flat convergence for Euclidean integer rectifiable currents amounts just to weak convergence. The purpose of the present paper is to extend this result to integral currents in complete metric spaces admitting a local cone type inequality. This includes for example all Banach spaces and complete CAT(κ)-spaces, κ ∈ R. Th...

Covering Spaces

Theory of Covering Spaces

Introduction. In this paper I study covering spaces in which the base space is an arbitrary topological space. No use is made of arcs and no assumptions of a global or local nature are required. In consequence, the fundamental group ir(X, Xo) which we obtain frequently reflects local properties which are missed by the usual arcwise group iri(X, Xo). We obtain a perfect Galois theory of covering...

CONVERGENCE APPROACH SPACES AND APPROACH SPACES AS LATTICE-VALUED CONVERGENCE SPACES

We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

Monoidal closedness of $L$-generalized convergence spaces

In this paper, it is shown that the category of stratified $L$-generalized convergence spaces is monoidal closed if the underlying truth-value table $L$ is a complete residuated lattice. In particular, if the underlying truth-value table $L$ is a complete Heyting Algebra, the Cartesian closedness of the category is recaptured by our result.