A note on Fréchet 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 ideals of compact sets
Solecki has shown that a broad natural class of ideals of compact sets can be represented through the ideal of nowhere dense subsets of a closed subset of the hyperspace of compact sets. In this note we show that the closed subset in this representation can be taken to be closed upwards.
A note on generalized Souslin's problem
A note on generic chaos
We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.
A note on hyperconnected sets
A note on hyperspaces and the fixed point property
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 k-c-semistratifiable spaces and strong -spaces
Recall that a space is a c-semistratifiable (CSS) space, if the compact sets of are -sets in a uniform way. In this note, we introduce another class of spaces, denoting it by k-c-semistratifiable (k-CSS), which generalizes the concept of c-semistratifiable. We discuss some properties of k-c-semistratifiable spaces. We prove that a -space is a k-c-semistratifiable space if and only if has a function which satisfies the following conditions: (1) For each , and for each . (2) If a...
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 Locally Almost Paracompact Spaces
A note on mappings of Baire spaces
A note on maximally resolvable spaces.
A note on measurability of trajectories of a stochastic process
A note on metrically inward mappings
A note on metrics and tolerances
A note on minimal dynamical systems
A note on monotone countable paracompactness
We show that a space is MCP (monotone countable paracompact) if and only if it has property , introduced by Teng, Xia and Lin. The relationship between MCP and stratifiability is highlighted by a similar characterization of stratifiability. Using this result, we prove that MCP is preserved by both countably biquotient closed and peripherally countably compact closed mappings, from which it follows that both strongly Fréchet spaces and q-space closed images of MCP spaces are MCP. Some results on...