Compactifying the space of homeomorphisms
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.
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
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
Conditions which ensure that a simple map does not raise dimension
The present paper deals with those continuous maps from compacta into metric spaces which assume each value at most twice. Such maps are called here, after Borsuk and Molski (1958) and as in our previous paper (1990), simple. We investigate the possibility of decomposing a simple map into essential and elementary factors, and the so-called splitting property of simple maps which raise dimension. The aim is to get insight into the structure of those compacta which have the property that simple maps...
Confluent and related mappings
Confluent local expansions
Confluent mappings of fans [Book]
Congruences on semigroups of continuous selfmaps.
Connected CM-homomorphisms into semigroups of closed binary relations on hereditarily locally connected cont inua.
Connected economically metrizable spaces
A topological space is non-separably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a non-separably connected complete metric space X under a monotone quotient map. The metric of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set does not exceed the density of A, . The construction of the space X determines a functor : Top...