The Schauder conjecture that every compact convex subset of a metric linear space has the
fixed‐point property was recently established by Cauty (2001). This paper elaborates on …

Motivated by the randomized version of the classical Bolzano–Weierstrass theorem, in this
paper we first introduce the notion of a random sequentially compact set in a random …

This paper focuses on the relation between the fixed point property for continuous mappings
and a discrete lion and man game played in a strongly convex domain. Our main result …

The strongly universal property was introduced by M. Bestvina and J. Mogilski in [BM] to
characterize topologically certain incomplete infinite-dimensional absolute retracts. This …

Let X be a Banach space and let C be a closed convex bounded subset of X. It is proved that
C is weakly compact if, and only if, C has the generic fixed point property (G-FPP) for the …

The well-known theorem on the uniformalization of topological properties [1] has been
strengthened and generalized to the case of a countable family of properties given by …

The class of metrizable spaces M with the following approximation property is introduced
and investigated: M∈ AP (n, 0) if for every ε> 0 and a map g: In→ M there exists a 0 …

It is shown that if f: X→ Y is a perfect map between metrizable spaces and Y is a C-space,
then the function space C (X, I) with the source limitation topology contains a dense Gδ …

In [12] Ceoghegan and Summerhill constructed the га-dimensional universal
pseudoboundary (jkn of the fc-dimensional Euclidean space Ш, к^ 0< n< к, к> 1, as an Лч …

Random normed modules (RN modules) are a random generalization of ordinary normed
spaces, which are usually endowed with the two kinds of topologies—the (ε, λ)–topology …