Pseudo-contractibility of chainable continua

Mapping Chainable Continua onto Dendroids

We prove that every chainable continuum can be mapped into a dendroid such that all point-inverses consist of at most three points. In particular, it follows that there exists a finite-to-one map from a hereditarily indecomposable continuum (the pseudoarc) onto hereditarily decomposable continuum. This answers a question by J. Krasinkiewicz.

The nonexistence of expansive homeomorphisms of chainable continua

A homeomorphism f : X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x 6= y, then there is an integer n ∈ Z such that d(f(x), f(y)) > c. In this paper, we prove that if a homeomorphism f : X → X of a continuum X can be lifted to an onto map h : P → P of the pseudoarc P , then f is not expansive. As a corollary, we prove that there are no expansive ho...

Pseudo-contractibility Of Weighted L−Algebras

Let G be a locally compact group, 1 < p < ∞ and let ω be a weight function on G. Recently, we introduced the Lebesgue weighted L−algebra L ω (G). Here, we establish necessary and sufficient conditions for L ω (G) to be φ−contractible, pseudo-contractible or contractible. Moreover we give some similar results about L(G,ω).

Topology Proceedings 7 (1982) pp. 391-393: QUESTIONS ON HOMEOMORPHISM GROUPS OF CHAINABLE AND HOMOGENEOUS CONTINUA

A1-contractibility and topological contractibility

These notes are an extended transcript of two lectures given at the University of Ottawa during the workshop “Group actions, generalized cohomology theories, and affine algebraic geometry." The first lecture was a general introduction to A1-homotopy theory focusing on motivating the choice of definitions in the construction, together with a definition of A1-contractible spaces. The second lectu...