Weak contractibility and hyperspaces
Weak L-structures and dimension
Weak orderability of second countable spaces
We demonstrate that a second countable space is weakly orderable if and only if it has a continuous weak selection. This provides a partial positive answer to a question of van Mill and Wattel.
Weak orderability of some spaces which admit a weak selection
We show that if a Hausdorff topological space satisfies one of the following properties: a) has a countable, discrete dense subset and is hereditarily collectionwise Hausdorff; b) has a discrete dense subset and admits a countable base; then the existence of a (continuous) weak selection on implies weak orderability. As a special case of either item a) or b), we obtain the result for every separable metrizable space with a discrete dense subset.
Weak selections and weak orderability of function spaces
It is proved that for a zero-dimensional space , the function space has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space , the function space is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides a partial...
Weak-chainability of tree-like continua and the combinatorial properties of mappings
Weakly chainable circle-like continua
Weakly confluent mappings and a classification of continua
Weakly infinite-dimensional compactifications and countable-dimensional compactifications
In this paper we give a characterization of a separable metrizable space having a metrizable S-weakly infinite-dimensional compactification in terms of a special metric. Moreover, we give two characterizations of a separable metrizable space having a metrizable countable-dimensional compactification.
Weakly smooth dendroids
Weight and metrizability of inverses under hereditarily irreducible mappings.
Whitney maps-a non-metric case
It is shown that there is no Whitney map on the hyperspace for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).
Whitney Preserving Maps onto Dendrites
We prove the following results. (i) Let X be a continuum such that X contains a dense arc component and let D be a dendrite with a closed set of branch points. If f:X → D is a Whitney preserving map, then f is a homeomorphism. (ii) For each dendrite D' with a dense set of branch points there exist a continuum X' containing a dense arc component and a Whitney preserving map f':X' → D' such that f' is not a homeomorphism.
Whitney properties
Wide tree-like spaces have a fixed point
Zero-dimensional open mappings which increase dimension
Zur Lage null- und eindimensionaler Punktmengen im
κ-compactness, extent and the Lindelöf number in LOTS
We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.
Аксиоматика размерности метрических пространств
Аппроксимационные и фундаментальные ретракты