The convergence-theoretic approach to weakly first countable spaces and symmetrizable spaces
نویسندگان
چکیده
منابع مشابه
CONVERGENCE APPROACH SPACES AND APPROACH SPACES AS LATTICE-VALUED CONVERGENCE SPACES
We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...
متن کاملconvergence approach spaces and approach spaces as lattice-valued convergence spaces
we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...
متن کاملCH and first countable , countably compact spaces ✩
We show that it is consistent with the Continuum Hypothesis that first countable, countably compact spaces with no uncountable free sequences are compact. As a consequence, we get that CH does not imply the existence of a perfectly normal, countably compact, non-compact space, answering a question of Nyikos (Question 287 in the numbering of van Mill and Reed, Open Problems in Topology, Elsevier...
متن کاملOn Radon measures on first-countable spaces
It is shown that every Radon measure on a first-countable Hausdorff space is separable provided ω1 is a precaliber of every measurable algebra. As the latter is implied by MA(ω1), the result answers a problem due to D. H. Fremlin. Answering the problem posed by D. H. Fremlin ([4], 32R(c)), we show in this note that, assuming (∗) ω1 is a precaliber of every measurable Boolean algebra, every Rado...
متن کاملOn nowhere first-countable compact spaces with countable π-weight
The minimum weight of a nowhere first-countable compact space of countable π-weight is shown to be κB, the least cardinal κ for which the real line R can be covered by κ many nowhere dense sets.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematica Slovaca
سال: 2019
ISSN: 1337-2211,0139-9918
DOI: 10.1515/ms-2017-0213