A Nielsen number for fixed points and near points of small multifunctions
A non-archimedean Dugundji extension theorem
We prove a non-archimedean Dugundji extension theorem for the spaces of continuous bounded functions on an ultranormal space with values in a non-archimedean non-trivially valued complete field . Assuming that is discretely valued and is a closed subspace of we show that there exists an isometric linear extender if is collectionwise normal or is Lindelöf or is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace of an ultraregular...
A note about the almost continuity
A note on a paper of J.A. Guthrie and M. Henry
A note on almost continuous mappings and Baire spaces.
A note on almost contra-precontinuous functions.
A note on Ascol's theorem for spaces of multifunctions.
A note on Baire isomorphism
A note on bi-contra-continuous maps.
A note on characterizations of compactness.
A note on condensations of onto compacta
A condensation is a one-to-one continuous mapping onto. It is shown that the space of real-valued continuous functions on in the topology of pointwise convergence very often cannot be condensed onto a compact Hausdorff space. In particular, this is so for any non-metrizable Eberlein compactum (Theorem 19). However, there exists a non-metrizable compactum such that condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated.
A note on connectedness in Cartesian closed categories.
A note on continuous linear mappings between function spaces
A note on dense subspaces of dyadic compact spaces
A note on functions with a closed graph
A note on -metrizable spaces
In this paper, the relationships between metric spaces and -metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems.
A note on inverse limits of continuous images of arcs.
The main purpose of this paper is to prove some theorems concerning inverse systems and limits of continuous images of arcs. In particular, we shall prove that if X = {Xa, pab, A} is an inverse system of continuous images of arcs with monotone bonding mappings such that cf (card (A)) ≠ w1, then X = lim X is a continuous image of an arc if and only if each proper subsystem {Xa, pab, B} of X with cf(card (B)) = w1 has the limit which is a continuous image of an arc (Theorem 18).
A note on inverse-preservations of regular open sets.
A note on linear mappings between function spaces
Arhangel’skiǐ proved that if and are completely regular spaces such that and are linearly homeomorphic, then is pseudocompact if and only if is pseudocompact. In addition he proved the same result for compactness, -compactness and realcompactness. In this paper we prove that if is a continuous linear surjection, then is pseudocompact provided is and if is a continuous linear injection, then is pseudocompact provided is. We also give examples that both statements do not hold...
A note on mappings of Baire spaces