On a metrization of the hyperspace of a metric space
On absolutely submetrizable spaces
We introduce a notion of absolute submetrizability (= ``every Tychonoff subtopology is submetrizable'') and investigate its behavior under basic topological operations. The main result is an example of an absolutely submetrizable space that contains an uncountable set of isolated points (hence the space is neither separable nor hereditarily Lindelöf). This example is used to show that absolute submetrizability is not preserved by some topological operations, in particular, by free sums.
On AP and WAP spaces
Several remarks on the properties of approximation by points (AP) and weak approximation by points (WAP) are presented. We look in particular at their behavior in product and at their relationships with radiality, pseudoradiality and related concepts. For instance, relevant facts are: (a) There is in ZFC a product of a countable WAP space with a convergent sequence which fails to be WAP. (b) over -compact space is AP. Therefore AP does not imply even pseudoradiality in function spaces, while...
On closed mappings
On -property of strong spaces
It is shown that every strong space is a -space. In particular, it follows that every paracompact space is a -space.
On fine shape theory II
On movability and other similar shape properties
On semi-closed sets and semi-open sets and their applications
On shapes of topological spaces
On the inequivalence of the Borsuk and the H-shape theories for arbitrary metric spaces
On the product of a perfect paracompact space and a countable product of scattered paracompact spaces
On thin-tall scattered spaces
On weakly monotonically monolithic spaces
In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a -space. Thus most known conclusions on -spaces can be obtained by this conclusion. As a corollary, we have that if a regular space is sequential and has a point-countable -network then is a -space.