A note on open mappings of irreducible continua
A note on singular homology groups of infinite products of compacta
Let n be an integer with n ≥ 2 and be an infinite collection of (n-1)-connected continua. We compare the homotopy groups of with those of (Σ denotes the unreduced suspension) via the Freudenthal Suspension Theorem. An application to homology groups of the countable product of the n(≥ 2)-sphere is given.
A note on the paper ``Smoothness and the property of Kelley''
Let be a continuum. In Proposition 31 of J.J. Charatonik and W.J. Charatonik, Smoothness and the property of Kelley, Comment. Math. Univ. Carolin. 41 (2000), no. 1, 123–132, it is claimed that , where is the set of points at which is locally connected and, for , if and only if is smooth at with respect to . In this paper we show that such equality is incorrect and that the correct equality is , where is the set of points at which is connected im kleinen. We also use the correct...
A note on topological m-spaces
A note on -closed sets and inverse limits.
A positional characterization of the (n-1)-dimensional Sierpiński curve in (η ≠ 4)
A remark on the Moore theorem.
A retractible non-locally connected dendroid
A retractible non-locally connected dendroid is constructed.
A singular plane curve
A SURVEY OF SEMIGROUPS OF CONTINUOUS SELFMAPS.
A universal planar completely regular continuum
We construct a universal planar completely regular continuum. This gives a positive answer to a problem posed by J. Krasinkiewicz (1986).
A weakly chainable uniquely arcwise connected continuum without the fixed point property
A continuum is a metric compact connected space. A continuum is chainable if it is an inverse limit of arcs. A continuum is weakly chainable if it is a continuous image of a chainable continuum. A space X is uniquely arcwise connected if any two points in X are the endpoints of a unique arc in X. D. P. Bellamy asked whether if X is a weakly chainable uniquely arcwise connected continuum then every mapping f: X → X has a fixed point. We give a counterexample.
AANR spaces and absolute retracts for tree-like continua
Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, -dendroids, dendroids, arc-like continua and arc-like -dendroids is an approximative absolute...
Absolute end points and their mapping properties.
Absolute end points of irreducible continua
A concept of an absolute end point introduced and studied by Ira Rosenholtz for arc-like continua is extended in the paper to be applied arbitrary irreducible continua. Some interrelations are studied between end points, absolute end points and points at which a given irreducible continuum is smooth.
Absolute fixed-point sets in compacta
Absolute n-fold hyperspace suspensions
The notion of an absolute n-fold hyperspace suspension is introduced. It is proved that these hyperspaces are unicoherent Peano continua and are dimensionally homogeneous. It is shown that the 2-sphere is the only finite-dimensional absolute 1-fold hyperspace suspension. Furthermore, it is shown that there are only two possible finite-dimensional absolute n-fold hyperspace suspensions for each n ≥ 3 and none when n = 2. Finally, it is shown that infinite-dimensional absolute n-fold hyperspace suspensions...
Absolutely terminal continua and confluent mappings
Interrelations between three concepts of terminal continua and their behaviour, when the underlying continuum is confluently mapped, are studied.
Acknowledgement concerning two papers on rational dimension
Almost convex metrics and Peano compactifications.