For a Tychonoff space $X$, we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence.  We study a functional characterization of the covering property of Hurewicz.

The geometries studied in this paper are obtained from buildings of spherical type by removing all chambers at non-maximal distance from a given element or flag. I consider a number of special cases of the above construction chosen among those which most frequently appear in the literature, proving that the resulting geometry is always simply connected but for three cases of small rank defined ...

We study here the poset DP (X) of density preserving continuous maps defined on a Hausdorff sapce X and show that it is a complete lattice for a compact Hausdorff space without isolated points. We further show that for countably compact T3 spaces X and Y without isolated points, DP (X) and DP (Y ) are order isomorphic if and only if X and Y are homeomorphic. Finally, Magill’s result on the rema...

In 1966, Michael [11] introduced the concept of compact-covering maps. Since many important kinds of maps are compact-covering, such as closed maps on paracompact spaces, much work has been done to seek the characterizations of metric spaces under various compact-covering maps, for example, compact-covering (open) s-maps, pseudosequence-covering (quotient) s-maps, sequence-covering (quotient) s...

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.

In this paper, we try to give as comprehensive an account of covering spaces as possible. We cover the usual material on classification and deck transformations, and also show how to perceive the subject from a more abstract categorical view point. The reader is assumed to possess a working knowledge of basic topology and category theory.

This paper defines a symplectic form on the infinite dimensional Fréchet manifold of framed curves of fixed length over a three dimensional simply connected Riemannian manifold of constant curvature. The framed curves are anchored at the initial point and are further constrained by the condition that the tangent vector of the projected curve coincides with the first leg of the orthonormal frame...

We present a new proof of Chern-Ji's mapping theorem on a strongly pseudoconvex domain with differentiable spherical boundary. We show that a proper holomorphic self mapping of a strongly pseudoconvex domain with the real analytic boundary is biholomorphic. We shall show that a bounded domain D is biholomorphic to an open ball B n+1 whenever the boundary bD is locally biholomorphic to the bound...

It has long been realized that the presence of a Reebless foliation in a compact 3-manifold M reveals useful topological information about M . By Novikov [No65], M is irreducible with infinite fundamental group. By Palmeira [Pa78], M has universal cover R. Building on work of Thurston and Gabai and Kazez [Ga98, GK98], Calegari [Ca] has shown that if M is also atoroidal, then π1(M) is Gromov neg...

We develop a diagrammatic language for symmetric product orbifolds of two-dimensional conformal field theories. Correlation functions of twist operators are written as sums of diagrams: each diagram corresponds to a branched covering map from a surface where the fields are single-valued to the base sphere where twist operators are inserted. This diagrammatic language facilitates the study of th...