On bicompacta which are unions of two subspaces of a certain type
On Blumberg type spaces
On category-raising and dimension-raising open mappings with discrete fibers
On concentrated sets
On non-separable 0-dimensional metrizable spaces
On sequence-covering --images of locally separable metric spaces
On the almost Lindelöf property in products of separable metric spaces
On the inverse image of Baire spaces.
On the -Baire property
In this note we show the following theorem: “Let be an almost -discrete space, where is a regular cardinal. Then is -Baire iff it is a -Baire space and every point- open cover of such that is locally- at a dense set of points.” For we obtain a well-known characterization of Baire spaces. The case is also discussed.
On Weakly Measurable Functions
We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".