A continuum without the fixed point property which is quasihomeomorphic with an AR-set
A continuum such that is not continuously homogeneous
A metric continuum is said to be continuously homogeneous provided that for every two points there exists a continuous surjective function such that . Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum such that the hyperspace of subcontinua of , , is not continuously homogeneous.
A correction to my paper:"Some topological extensions of plane geometry"
A countable connected Urysohn space with a dispersion point that is regular almost everywhere
A counterexample in non-metric continua theory
A counter-example on unicoherent Peano spaces
A decomposition theorem for a class of continua for which the set function T is continuous
We prove a decomposition theorem for a class of continua for which F. B.. Jones's set function 𝓣 is continuous. This gives a partial answer to a question of D. Bellamy.
A decomposition theorem for collections of universal subcontinua
A fixed point principle for locally expansive multifunctions
A fixed point theorem for continua which are hereditarily divisible by points
A fixed point theorem for plane homeomorphisms
A fixed-point anomaly in the plane
We define an unusual continuum M with the fixed-point property in the plane ℝ². There is a disk D in ℝ² such that M ∩ D is an arc and M ∪ D does not have the fixed-point property. This example answers a question of R. H. Bing. The continuum M is a countable union of arcs.
A hereditarily indecomposable, hereditarily non-chainable planar tree-like continuum
A hereditarily indecomposable non-metric Hausdorff continuum
A hit-and-miss topology for , Cₙ(X) and Fₙ(X)
A hit-and-miss topology () is defined for the hyperspaces , Cₙ(X) and Fₙ(X) of a continuum X. We study the relationship between and the Vietoris topology and we find conditions on X for which these topologies are equivalent.
A locally connected non-movable continuum that fails to separate
A metrization theorem for the product of ordered continua
A non-chainable plane continuum with span zero
A plane continuum is constructed which has span zero but is not chainable.
A note on cyclic subelement theory-reducibility of local connectedness and local simple connectedness
A note on inverse limits of continuous images of arcs.
The main purpose of this paper is to prove some theorems concerning inverse systems and limits of continuous images of arcs. In particular, we shall prove that if X = {Xa, pab, A} is an inverse system of continuous images of arcs with monotone bonding mappings such that cf (card (A)) ≠ w1, then X = lim X is a continuous image of an arc if and only if each proper subsystem {Xa, pab, B} of X with cf(card (B)) = w1 has the limit which is a continuous image of an arc (Theorem 18).