### Some productive classes of maps which arc related to confluent maps

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

A continuum means a compact connected metric space. For a continuum X, H(X) denotes the space of all homeomorphisms of X with the compact-open topology. It is well known that H(X) is a completely metrizable, separable topological group. J. Kennedy [8] considered a compactification of H(X) and studied its properties when X has various types of homogeneity. In this paper we are concerned with the compactification ${G}_{P}$ of the homeomorphism group of the pseudo-arc P, which is obtained by the method of...

We study the (n+1)st homotopy groups and the shape groups of the (n-1)-fold reduced and unreduced suspensions of the Hawaiian earring.

Let n be an integer with n ≥ 2 and ${X}_{i}$ be an infinite collection of (n-1)-connected continua. We compare the homotopy groups of $\Sigma \left({\prod}_{i}{X}_{i}\right)$ with those of ${\prod}_{i}\Sigma {X}_{i}$ (Σ denotes the unreduced suspension) via the Freudenthal Suspension Theorem. An application to homology groups of the countable product of the n(≥ 2)-sphere is given.

For the n-dimensional Hawaiian earring ${\mathbb{H}}_{n},$ n ≥ 2, ${\pi}_{n}({\mathbb{H}}_{n},o)\simeq {\mathbb{Z}}^{\omega}$ and ${\pi}_{i}({\mathbb{H}}_{n},o)$ is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CX ∨ CY be the one-point union with two points of the base spaces X and Y being identified to a point. Then ${H}_{n}\left(X\vee Y\right)\simeq {H}_{n}\left(X\right)\oplus {H}_{n}\left(Y\right)\oplus {H}_{n}\left(CX\vee CY\right)$ for n ≥ 1.

The main result says that nondiscrete, weakly closed, containing no nontrivial linear subspaces, additive subgroups in separable reflexive Banach spaces are homeomorphic to the complete Erdős space. Two examples of such subgroups in ${\ell}^{1}$ which are interesting from the Banach space theory point of view are discussed.

The Cantor set and the set of irrational numbers are examples of 0-dimensional, totally disconnected, homogeneous spaces which admit elegant characterizations and which play a crucial role in analysis and dynamical systems. In this paper we will start the study of 1-dimensional, totally disconnected, homogeneous spaces. We will provide a characterization of such spaces and use it to show that many examples of such spaces which exist in the literature in various fields are all homeomorphic. In particular,...

**Page 1**