On nearly strongly paracompact spaces.
is non-normal for any metrizable crowded space and an arbitrary point .
Let a space be Tychonoff product of -many Tychonoff nonsingle point spaces . Let Suslin number of be strictly less than the cofinality of . Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification . In particular, this is true if is either or and a cardinal is infinite and not countably cofinal.
The spaces in which every prime -ideal of is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces , such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime -ideal in is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in a -ideal? When is every nonregular (prime) -ideal in a -ideal? For...
The minimum weight of a nowhere first-countable compact space of countable -weight is shown to be , the least cardinal for which the real line can be covered by many nowhere dense sets.