Operations that Preserve the Covering Property of the Lifting Region

On category of co-coverings

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

Characterization of covering maps via path-lifting property

A continuous map between topological f : X → Y is said to satisfy the path-lifting property if for any path p : [0, 1] → Y and any x ∈ f(p(0)) there exists a lifting p̃ of the path p with the intitial value x, i.e. there exists a path p̃ such that f ◦ p̃ = p and p̃(0) = x. Similarly, a smooth map between Riemannian manifolds f : X → Y is said to satisfy the rectifiable path-lifting property if the ...

Schur-Pair Property and the Structure of Varietal Covering Groups

A COVERING PROPERTY IN PRINCIPAL BUNDLES

Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...

An example of idiosyncracy between topological coverings and analytic functions

We exhibit a locally biholomorphic mapping with simply connected image, which fails to be a topological covering. Introduction In [1], A.F.Beardon shows an example of a ’covering surface’ over the unit disc D ⊂ C, which is not a topological covering. We recall that a ’covering surface’ of a regionD ⊂ C, is a Riemann surface S admitting surjective conformal mapping onto D, whereas a continuous m...