Mapping arcwise connected continua onto cyclic continua
Mapping hierarchy for dendrites [Book]
Mapping theorems on -spaces
In this paper we improve some mapping theorems on -spaces. For instance we show that an -space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an -space is preserved by a closed and open map.
Mappings and decompositions of continuity on almost Lindelöf spaces.
Mappings covered by products and pinched products
Mappings of terminal continua.
Mappings on compact metric spaces
Mappings on manifolds
Mappings on -paracompact spaces.
Mappings related to confluence
Necessary and sufficient conditions are found in the paper for a mapping between continua to be monotone, confluent, semi-confluent, joining, weakly confluent and pseudo-confluent. Three lists of these conditions are presented. Two are formulated in terms of components and of quasi-components, respectively, of connected closed subsets of the range space, while the third one in terms of connectedness between subsets of the domain space. Some basic relations concerning these concepts are studied.
Mappings with 1-dimensional absolute neighborhood retract fibers
Metacompactness and the class MOBI
Metrizability of inverse images of metric spaces under open perfect and 0-dimensional mappings
Minimal bi-Lipschitz embedding dimension of ultrametric spaces
We prove that an ultrametric space can be bi-Lipschitz embedded in if its metric dimension in Assouad’s sense is smaller than n. We also characterize ultrametric spaces up to bi-Lipschitz homeomorphism as dense subspaces of ultrametric inverse limits of certain inverse sequences of discrete spaces.
Minimal class generated by open compact and perfect mappings
Monotone homogeneity of dendrites
Sufficient as well as necessary conditions are studied for a dendrite or a dendroid to be homogeneous with respect to monotone mappings. The obtained results extend ones due to H. Kato and the first named author. A number of open problems are asked.
Monotone retractions and depth of continua
It is shown that for every two countable ordinals and with there exist -dendroids and whose depths are and respectively, and a monotone retraction from onto . Moreover, the continua and can be either both arclike or both fans.
Monotonic mappings on ordered sets, a class of inequalities with finite differences and fixed points.
More on generalized homeomorphisms in topological spaces.
Multiplicative sequences for universal sequences of mappings.