Productively Lindelöf spaces may all be D
نویسنده
چکیده
We give easy proofs that a) the Continuum Hypothesis implies that if the product of X with every Lindelöf space is Lindelöf, then X is a D-space, and b) Borel’s Conjecture implies every Rothberger space is Hurewicz.
منابع مشابه
Weak Covering Properties and Selection Principles
No convenient internal characterization of spaces that are productively Lindelöf is known. Perhaps the best general result known is Alster’s internal characterization, under the Continuum Hypothesis, of productively Lindelöf spaces which have a basis of cardinality at most א1. It turns out that topological spaces having Alster’s property are also productively weakly Lindelöf. The weakly Lindelö...
متن کاملSet-theoretic Problems Concerning Lindelöf Spaces
I survey problems concerning Lindelöf spaces which have partial settheoretic solutions. Lindelöf spaces, i.e. spaces in which every open cover has a countable subcover, are a familiar class of topological spaces. There is a significant number of (mainly classic) problems concerning Lindelöf spaces which are unsolved, but have partial set-theoretic solutions. For example, consistency is known bu...
متن کاملOn Productively Lindelöf Spaces
We study conditions on a topological space that guarantee that its product with every Lindelöf space is Lindelöf. The main tool is a condition discovered by K. Alster and we call spaces satisfying his condition Alster spaces. We also study some variations on scattered spaces that are relevant for this question.
متن کاملLindelöf indestructibility, topological games and selection principles
Arhangel’skii proved that if a first countable Hausdorff space is Lindelöf, then its cardinality is at most 20 . Such a clean upper bound for Lindelöf spaces in the larger class of spaces whose points are Gδ has been more elusive. In this paper we continue the agenda started in [50], of considering the cardinality problem for spaces satisfying stronger versions of the Lindelöf property. Infinit...
متن کاملProducts of Lindelöf T2-spaces are Lindelöf — in some models of ZF
The stability of the Lindelöf property under the formation of products and of sums is investigated in ZF (= Zermelo-Fraenkel set theory without AC, the axiom of choice). It is • not surprising that countable summability of the Lindelöf property requires some weak choice principle, • highly surprising, however, that productivity of the Lindelöf property is guaranteed by a drastic failure of AC, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011