Product Property on Generalized Lindelöf Spaces
نویسندگان
چکیده
منابع مشابه
On 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 کاملSome results on linearly Lindelöf spaces ∗
Some new results about linearly Lindelöf spaces are given here. It is proved that if X is a space of countable spread and X = Y ∪ Z, where Y and Z are meta-Lindelöf spaces, then X is linearly Lindelöf. Moreover, we give a positive answer to a problem raised by A.V. Arhangel’skii and R.Z. Buzyakova.
متن کاملON GENERALIZED n-INNER PRODUCT SPACES
(i) ∥x1, x2, . . . , xn∥ = 0 if any only if x1, x2, . . . , xn are linearly dependent, (ii) ∥x1, x2, . . . , xn∥ is invariant under any permutation, (iii) ∥x1, x2, . . . , axn∥ = |a| ∥x1, x2, . . . , xn∥, for any a ∈ R (real), (iv) ∥x1, x2, . . . , xn−1, y + z∥ = ∥x1, x2, . . . , xn−1, y∥ + ∥x1, x2, . . . , xn−1, z∥ is called an n-norm on X and the pair (X, ∥•, . . . , •∥) is called n-normed li...
متن کاملProductively Lindelöf spaces may all be D
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.
متن کاملLindelöf spaces C ( X ) over topological groups
Theorem 1 proves (among the others) that for a locally compact topological group X the following assertions are equivalent: (i) X is metrizable and s-compact. (ii) CpðXÞ is analytic. (iii) CpðXÞ is K-analytic. (iv) CpðXÞ is Lindelöf. (v) CcðX Þ is a separable metrizable and complete locally convex space. (vi) CcðX Þ is compactly dominated by irrationals. This result supplements earlier results ...
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: ISRN Mathematical Analysis
سال: 2011
ISSN: 2090-4657,2090-4665
DOI: 10.5402/2011/843480