A non-Tychonoff relatively normal subspace
This paper presents a new consistent example of a relatively normal subspace which is not Tychonoff.
A normal space X for which X×I is not normal
A note on collectionwise normality and product spaces
A note on dense subspaces of dyadic compact spaces
A note on exponentiation in regular locales
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 neighborhood product spaces
A note on normal topological functors and extensions of transformations
A note on product of topological spaces (Preliminary communication)
A note on products of Fréchet spaces
A note on pseudobounded paratopological groups
Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if for every neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn). We show that every feebly compact (2-pseudocompact) pseudobounded (ω-pseudobounded) premeager paratopological group is a topological group. Also,we prove that if G is a totally ω-pseudobounded paratopological group such that G is a Lusin space, then is G a topological group....
A note on -embeddings
A note on separability of the Fell-hyperspace topology
A note on spaces with countable extent
Let be a topological property. A space is said to be star P if whenever is an open cover of , there exists a subspace with property such that . In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa.
A note on the locally Hausdorff property
A note on the non-emptiness of the limit of approximate systems
Short proofs of the fact that the limit space of a non-gauged approximate system of non-empty compact uniform spaces is non-empty and of two related results are given.
A note on topological groups and their remainders
In this note we first give a summary that on property of a remainder of a non-locally compact topological group in a compactification makes the remainder and the topological group all separable and metrizable. If a non-locally compact topological group has a compactification such that the remainder of belongs to , then and are separable and metrizable, where is a class of spaces which satisfies the following conditions: (1) if , then every compact subset of the space is a...
A note on -closed sets and inverse limits.
A note to decompositions of real line
A Property Between Compact and Strongly Countably Compact