منابع مشابه
Products of ¿-spaces and Spaces of Countable Tightness
In this paper, we obtain results of the following type: if /: X -» Y is a closed map and X is some "nice" space, and Y2 is a &-space or has countable tightness, then the boundary of the inverse image of each point of Y is "small" in some sense, e.g., Lindelöf or «¿¡-compact. We then apply these results to more special cases. Most of these applications combine the "smallness" of the boundaries o...
متن کاملBernstein's Lethargy Theorem in Fréchet spaces
In this paper we consider Bernstein’s Lethargy Theorem (BLT) in the context of Fréchet spaces. Let X be an infinite-dimensional Fréchet space and let V = {Vn} be a nested sequence of subspaces of X such that Vn ⊆ Vn+1 for any n ∈ N and X = ⋃∞ n=1 Vn. Let en be a decreasing sequence of positive numbers tending to 0. Under an additional natural condition on sup{dist(x, Vn)}, we prove that there e...
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 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 کاملSeries expansions in Fréchet spaces and their duals, construction of Fréchet frames
Frames for Fréchet spaces XF with respect to Fréchet sequence spaces ΘF are studied and conditions, implying series expansions in XF and X ∗ F , are determined. If {gi}i=1 is a Θ0-frame for X0, we construct a sequence {Xs}s∈N0 , Xs ⊂ Xs−1, s ∈ N, for given ΘF , respectively a sequence {Θs}s∈N0 , Θs ⊂ Θs−1, s∈N, for given XF , so that {gi}i=1 is a pre-F -frame (or F -frame) for XF with respect t...
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: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.12.059