On Compact Hausdorff Spaces of Countable Tightness
نویسندگان
چکیده
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.
منابع مشابه
Closed mapping theorems on k-spaces with point-countable k-networks
We prove some closed mapping theorems on k-spaces with point-countable k-networks. One of them generalizes Lašnev’s theorem. We also construct an example of a Hausdorff space Ur with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a k-space X with a point-countable k-network admitting a closed surjection which is not compac...
متن کاملPfa(s) and Countable Tightness
Todorcevic introduced the forcing axiom PFA(S) and established many consequences. We contribute to this project. In particular, we consider status under PFA(S) of two important consequences of PFA concerning spaces of countable tightness. In particular we prove that the existence of a Souslin tree does not imply the existence of a compact non-sequential space of countable tightness. We contrast...
متن کاملA new view on fuzzy automata normed linear structure spaces
In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...
متن کاملCompact Monotonically Metacompact Spaces Are Metrizable
Monotonically metacompact spaces were recently introduced as an extension of the concept of monotonically compact spaces. In this note we answer a question of Popvassilev, and Bennett, Hart, and Lutzer, by showing that every compact, Hausdorff, monotonically (countably) metacompact space is metrizable. We also show that certain countable spaces fail to be monotonically (countably) metacompact.
متن کاملTopology Proceedings TIGHTNESS IN σ-COMPACT SPACES
In 1993 Arhangelskii and Stavrova de ned the notion of the k-tightness number of a space and its hereditary version. They proved that the hereditary k-tightness of a compact space is equal to the standard notion of tightness. Out of this grew the notion of what one might call σ-compact tightness: the closure of a set is the union of the closures of all its σ-compact subsets. We contribute to th...
متن کامل