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We construct a space having the properties in the title, and with the same technique, a countably compact topological group which is not absolutely countably compact.
We exhibit a metric continuum X and a polyhedron P such that the Cartesian product X × P fails to be the product of X and P in the shape category of topological spaces.
We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, -stable and -monolithic. It is also established that any Sokolov compact space is Fréchet-Urysohn and the space is Lindelöf. We prove that any Sokolov space with a -diagonal has a countable network and obtain some cardinality restrictions on subsets...
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.
We observe the existence of a -compact, separable topological group and a countable topological group such that the tightness of is countable, but the tightness of is equal to .
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