All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 52

Showing per page

Productivity of coreflective classes of topological groups

Horst Herrlich, Miroslav Hušek (1999)

Commentationes Mathematicae Universitatis Carolinae

Every nontrivial countably productive coreflective subcategory of topological linear spaces is κ -productive for a large cardinal κ (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal κ , there are coreflective subcategories that are κ -productive and not κ + -productive (see [8]). From certain points of view, the category of topological groups lies in between those categories above and we shall show that the corresponding results on productivity of coreflective subcategories...

Products of Baire spaces revisited

László Zsilinszky (2004)

Fundamenta Mathematicae

Generalizing a theorem of Oxtoby, it is shown that an arbitrary product of Baire spaces which are almost locally universally Kuratowski-Ulam (in particular, have countable-in-itself π-bases) is a Baire space. Also, partially answering a question of Fleissner, it is proved that a countable box product of almost locally universally Kuratowski-Ulam Baire spaces is a Baire space.

Products of k -spaces, and questions

Yoshio Tanaka (2003)

Commentationes Mathematicae Universitatis Carolinae

As is well-known, every product of a locally compact space with a k -space is a k -space. But, the product of a separable metric space with a k -space need not be a k -space. In this paper, we consider conditions for products to be k -spaces, and pose some related questions.

Products of Lindelöf T 2 -spaces are Lindelöf – in some models of ZF

Horst Herrlich (2002)

Commentationes Mathematicae Universitatis Carolinae

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, • amusing that finite summability of the Lindelöf property takes place if either some weak choice principle...

Products of non- σ -lower porous sets

Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

In the present article we provide an example of two closed non- σ -lower porous sets A , B ⊆ ℝ such that the product A × B is lower porous. On the other hand, we prove the following: Let X and Y be topologically complete metric spaces, let A ⊆ X be a non- σ -lower porous Suslin set and let B ⊆ Y be a non- σ -porous Suslin set. Then the product A × B is non- σ -lower porous. We also provide a brief summary of some basic properties of lower porosity, including a simple characterization of Suslin non- σ -lower porous sets in topologically...

Currently displaying 21 – 40 of 52