Compactifying the space of homeomorphisms
Compactly generated shape theories
Compactness and extreme points of the set of quasi-measure extensions of a quasi-measure [Book]
Complexity of curves
We show that each of the classes of hereditarily locally connected, finitely Suslinian, and Suslinian continua is Π₁¹-complete, while the class of regular continua is Π₀⁴-complete.
Components and inductive dimensions of compact spaces
Composant-like decompositions
The body of this paper falls into two independent sections. The first deals with the existence of cross-sections in -decompositions. The second deals with the extensions of the results on accessibility in the plane.
Composants of the horseshoe
The horseshoe or bucket handle continuum, defined as the inverse limit of the tent map, is one of the standard examples in continua theory as well as in dynamical systems. It is not arcwise connected. Its arcwise components coincide with composants, and with unstable manifolds in the dynamical setting. Knaster asked whether these composants are all homeomorphic, with the obvious exception of the zero composant. Partial results were obtained by Bellamy (1979), Dębski and Tymchatyn (1987), and Aarts...
Compositions of confluent mappings and some other classes of functions
Compositions of simple maps
A map (= continuous function) is of order ≤ k if each of its point-inverses has at most k elements. Following [4], maps of order ≤ 2 are called simple. Which maps are compositions of simple closed [open, clopen] maps? How many simple maps are really needed to represent a given map? It is proved herein that every closed map of order ≤ k defined on an n-dimensional metric space is a composition of (n+1)k-1 simple closed maps (with metric domains). This theorem fails to be true...
Concerning a closed subset of a dendroid containing 2-ramification points
Concerning atriodic tree-like continua
Concerning closed quasi-orders on hereditarily unicoherent continua
Concerning decompositions of continua
Concerning hereditarily locally connected continua
Concerning indecomposable continua and upper semicontinuous collections of nondegenerate continua
Concerning irreducible continua of higher dimension
Concerning irreducible continua with homeomorphic layers
Concerning point sets with a special connectedness property, II
Concerning the structure of dendritic spaces
Concerning unicoherence of continua