Some theorems on equiconnected and locally equiconnected spaces

  title={Some theorems on equiconnected and locally equiconnected spaces},
  author={C. J. Himmelberg},
  journal={Transactions of the American Mathematical Society},
  • C. J. Himmelberg
  • Published 1 March 1965
  • Mathematics
  • Transactions of the American Mathematical Society


In the present paper we consider some extension properties for continuous maps in metric spaces and, using them, we develop in metric spaces some aspects of Granas theory of topological essentiality

Some generalizations on affine invariant points

In this note we prove a more general (and topological) version of Grunbaum's conjecture about affine invariant points. As an application of our result we show that, if we consider the action of the

Extending and improving conical bicombings

We prove that for every reversible conical bicombing $\sigma$ on a metric space $X$, there exists a conical bicombing on the injective hull of $X$ that extends $\sigma$. We also establish a

Spaces with convex geodesic bicombings

In the geometry of CAT(0) or Busemann spaces every pair of geodesics, call them α and β, have convex distance; meaning d ◦ (α, β) is a convex function I → R provided the geodesics are parametrized

Convex geodesic bicombings and hyperbolicity

A geodesic bicombing on a metric space selects for every pair of points a geodesic connecting them. We prove existence and uniqueness results for geodesic bicombings satisfying different convexity

Retracts and Extensors

  • K. Sakai
  • Mathematics, Computer Science
  • 2013
A subset A of a space X is called a retract of X if there is a map r : X→A such that r | A = id, which is called a retraction. As is easily observed, every retract of a space X is closed in X. A

Extending continuous functions

We examine conditions on a (compact metrizable) space $X$ such that for any space $Y$ and closed subspace $Z$, the set of continuous functions from $Z$ to $X$ which extend to $Y$ is either open or

Une généralisation de la conjecture de point fixe de Schauder

We prove the following generalisation of Schauder's fixed point conjecture: Let $C_1,...,C_n$ be convex subsets of a Hausdorff topological vector space. Suppose that the $C_i$ are closed in



Retraction and extension of mappings of metric and nonmetric spaces

1. The two kinds of topological spaces that are called absolute retracts and absolute neighborhood retracts, were originally defined by BO~SUK ([5], [6]) for compact metric spaces. Later on these

Absolute neighborhood retracts and local connectedness in arbitrary metric spaces

© Foundation Compositio Mathematica, 1956-1958, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: // implique l’accord avec les

Some theorems on absolute neighborhood retracts

1. In this paper we shall s tudy A1NR's (absolute neighborhood retracts). The general problem will be as follows. Suppose we have proved that all ANR's have a certain property. Then we may ask, if

On fibre spaces. II

This paper is primarily concerned with fibre mappings into an absolute neighborhood retract. Theorem 3 is a converse of the covering homotopy theorem; it characterizes fibre mappings (into a compact