Remarks on non-planable dendroids
In this paper, we prove that each sequence-covering and boundary-compact map on -metrizable spaces is 1-sequence-covering. Then, we give some relationships between sequence-covering maps and 1-sequence-covering maps or weak-open maps, and give an affirmative answer to the problem posed by F.C. Lin and S. Lin in [Lin.F.C.and.Lin.S-2011].
A space is strongly star-Menger if for each sequence of open covers of , there exists a sequence of finite subsets of such that is an open cover of . In this paper, we investigate the relationship between strongly star-Menger spaces and related spaces, and also study topological properties of strongly star-Menger spaces.
2000 Mathematics Subject Classification: 54C55, 54H25, 55M20.We introduce the class of algebraic ANRs. It is defined by replacing continuous maps by chain mappings in Lefschetz’s characterization of ANRs. To a large extent, the theory of algebraic ANRs parallels the classical theory of ANRs. Every ANR is an algebraic ANR, but the class of algebraic ANRs is much larger; the most striking difference between these classes is that every locally equiconnected metrisable space is an algebraic ANR, whereas...