In this paper, we prove that a space is a -metrizable space if and only if is a weak-open, and -image of a semi-metric space, if and only if is a strong sequence-covering, quotient, and -image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.
Let G be a compact group and X a G-ANR. Then X is a G-AR iff the H-fixed point set is homotopy trivial for each closed subgroup H ⊂ G.
In this paper fixed point theorems for maps with nonempty convex values and having the local intersection property are given. As applications several minimax inequalities are obtained.
We define and investigateCD Σ,Γ(K, E)-type spaces, which generalizeCD 0-type Banach lattices introduced in [1]. We state that the space CD Σ,Γ(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8].
Classical analytic spaces can be characterized as projections of Polish spaces. We prove analogous results for three classes of generalized analytic spaces that were introduced by Z. Frolík, D. Fremlin and R. Hansell. We use the technique of complete sequences of covers. We explain also some relations of analyticity to certain fragmentability properties of topological spaces endowed with an additional metric.
Given an ordered metric space (in particular, a Banach lattice) E, the generalized Helly space H(E) is the set of all increasing functions from the interval [0,1] to E considered with the topology of pointwise convergence, and E is said to have property (λ) if each of these functions has only countably many points of discontinuity. The main objective of the paper is to study those ordered metric spaces C(K,E), where K is a compact space, that have property (λ). In doing so, the guiding idea comes...