Abstract:
We study the open images of members of a countable family ℱ of dendrites. We show that only two members of ℱ are minimal and only one of them is unique minimal with respect to openmappings.

Abstract:
The lifting property of continua for classes of mappings isdefined. It is shown that the property is preserved under theinverse limit operation. The results, when applied to the class ofconfluent mappings, exhibit conditions under which the inducedmapping between hyperspaces is confluent. This generalizesprevious results in this topic.

Abstract:
The concept of a terminal continuum introduced in 1973 by G. R. Gordh Jr., for hereditarily unicoherent continua is extended to arbitrary continua. Mapping properties of these two concepts are investigated. Especially the invariance of terminality under mappings satisfying some special conditions is studied. In particular, we conclude that the invariance holds for atomic mappings.

Abstract:
For positive integers m and n, relations between (hereditary) m- and n-equivalence are studied, mostly for arc-like continua. Several structural and mapping problems concerning (hereditarily) finitely equivalent continua are formulated.

Abstract:
Relations between the fixed point properties for some classes of multifunctions of a compact Hausdorff space X, of a decomposition space X/D, where D is an upper semi-continuous decomposition of X, and of the members of D are studied. Results are applied to some special decompositions of metric continua.

Abstract:
A mapping f:X ￠ ’Y between continua X and Y is said to be atomic at a subcontinuumK of the domain X provided that f(K) is nondegenerate and K=f ￠ ’1(f(K)). The set of subcontinua at which a given mapping is atomic, considered as a subspace of the hyperspace of all subcontinua of X, is studied. The introduced concept is applied to get new characterizations of atomic and monotone mappings. Some related questions are asked.

Abstract:
The existence of an N-sequence in a continuum is a common obstruction that implies nonsmoothness, noncontractibility, nonselectibility, and nonexistence of any mean. The aim of the present paper is to investigate if some variants of the concept of an N-sequence also keep these properties. In particular, mapping properties of bend sets are studied.

Abstract:
Spaces which are metrizable completions of the space Q of rationals are described. A characterization of metrizable spaces having the same family of metrizable completions as Q is deduced.

Abstract:
Results concerning contractibility of curves (equivalently: of dendroids) are collected and discussed in the paper. Interrelations tetween various conditions which are either sufficient or necessary for a curve to be contractible are studied.

Abstract:
The question (raised in [7]) whether every homogeneous family of separators of a locally connected metrizable space Y, which is a partition of Y and has the continuum power, admits a continuous parametrization, is studied in the realm of locally connected curves.