An acyclic continuum that admits no mean
An algebraic and logical approach to continuous images
An arcwise connected continuum without nonboundary proper arcwise connected subcontinua.
An atomic map onto an arbitrary metric continuum
An atriodic tree-like continuum with positive span
An atriodic tree-like continuum with positive span which admits a monotone mapping to a chainable continuum
An Exactly Two-to-One Map from an Indecomposable Chainable Continuum
It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.
An example concerning the Whitehead Theorem in shape theory
An example for mappings related to confluence
Confluence of a mapping between topological spaces can be defined by several ways. J.J. Charatonik asked if two definitions of the confluence using the components and quasi-components are equivalent for surjective mappings with compact point inverses. We give the negative answer to this question in Example 2.1.
An example for mappings related to semi-confluence.
An example of 2-dimensional quasihomeomorphic sets
An example of a monostratiform λ-dendroid
An example of a non-compact locally compact arcwise connected metric space with the fixed point property
An example related to strongly pointwise self-homeomorphic dendrites
Such spaces in which a homeomorphic image of the whole space can be found in every open set are called self-homeomorphic. W.J. Charatonik and A. Dilks posed a problem related to strongly pointwise self-homeomorphic dendrites. We solve this problem negatively in Example 2.1.
An interesting plane dendroid
An uncountable collection of mutually exclusive planar atriodic tree-like continua with positive span
Another application of the Effros theorem to the pseudo-arc
Another semigroup characterization of the simple closed curve.
Approximating continua from within
Arc property of Kelley and absolute retracts for hereditarily unicoherent continua
We investigate absolute retracts for hereditarily unicoherent continua, and also the continua that have the arc property of Kelley (i.e., the continua that satisfy both the property of Kelley and the arc approximation property). Among other results we prove that each absolute retract for hereditarily unicoherent continua (for tree-like continua, for λ-dendroids, for dendroids) has the arc property of Kelley.