Moore-closed and first countable feebly compact extension spaces
نویسندگان
چکیده
منابع مشابه
CH 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 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 کاملFirst Countable, Countably Compact Spaces and the Continuum Hypothesis
We build a model of ZFC+CH in which every first countable, countably compact space is either compact or contains a homeomorphic copy of ω1 with the order topology. The majority of the paper consists of developing forcing technology that allows us to conclude that our iteration adds no reals. Our results generalize Saharon Shelah’s iteration theorems appearing in Chapters V and VIII of Proper an...
متن کاملSpaces with compact-countable weak-bases
In this paper, we establish the relationships between spaces with a compact-countable weak-base and spaces with various compact-countable networks, and give two mapping theorems on spaces with compact-countable weakbases. Weak-bases and g-first countable spaces were introduced by A.V.Arhangel’skii [1]. Spaces with a point-countable weak-base were discussed in [5,6], and spaces with a locally co...
متن کاملOn Compact Hausdorff Spaces of Countable Tightness
A general combinatorial theorem for countably compact, noncompact spaces is given under the Proper Forcing Axiom. It follows that compact Hausdorff spaces of countable tightness are sequential under PFA, solving the Moore-Mrowka Problem. Other applications are also given.
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: Topology and its Applications
سال: 1987
ISSN: 0166-8641
DOI: 10.1016/0166-8641(87)90054-x