## 26 Citations

### EXTENSION THEOREMS AND TOPOLOGICAL ESSENTIALITY IN α-WEAKLY CONVEX METRIC SPACES

- Mathematics
- 2009

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

- Mathematics
- 2020

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

- Mathematics
- 2020

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

- Mathematics
- 2016

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

- Mathematics
- 2014

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

- 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

- Mathematics
- 2012

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

- Mathematics
- 2012

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…

## References

SHOWING 1-10 OF 12 REFERENCES

### Retraction and extension of mappings of metric and nonmetric spaces

- Mathematics
- 1952

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

- Mathematics
- 1958

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

### Some theorems on absolute neighborhood retracts

- Mathematics
- 1951

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

- Mathematics
- 1943

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…