On a problem of Nogura about the product of Fréchet - Urysohn 〈 α 4 〉 - spaces
نویسنده
چکیده
Assuming Martin’s Axiom, we provide an example of two Fréchet-Urysohn 〈α4〉-spaces, whose product is a non-Fréchet-Urysohn 〈α4〉-space. This gives a consistent negative answer to a question raised by T. Nogura.
منابع مشابه
Workshop Lecture on Products of Fréchet Spaces
The general question, “When is the product of Fréchet spaces Fréchet?” really depends on the questions of when a product of α4 Fréchet spaces (also known as strongly Fréchet or countably bisequential spaces) is α4, and when it is Fréchet. Two subclasses of the class of strongly Fréchet spaces shed much light on these questions. These are the class of α3 Fréchet spaces and its subclass of א0-bis...
متن کاملFréchet-urysohn Spaces in Free Topological Groups
Let F (X) and A(X) be respectively the free topological group and the free Abelian topological group on a Tychonoff space X. For every natural number n we denote by Fn(X) (An(X)) the subset of F (X) (A(X)) consisting of all words of reduced length ≤ n. It is well known that if a space X is not discrete, then neither F (X) nor A(X) is Fréchet-Urysohn, and hence first countable. On the other hand...
متن کاملOn weakly bisequential spaces
Weakly bisequential spaces were introduced by A.V. Arhangel’skii [1], in this paper. We discuss the relations between weakly bisequential spaces and metric spaces, countably bisequential spaces, Fréchet-Urysohn spaces.
متن کاملFixed Point Theory for Admissible Type Maps with Applications
In this paper, assuming a natural sequentially compact conditionwe establish new fixed point theorems for Urysohn type maps between Fréchet spaces. In Section 2 we present new LeraySchauder alternatives, Krasnoselskii and Lefschetz fixed point theory for admissible type maps. The proofs rely on fixed point theory in Banach spaces and viewing a Fréchet space as the projective limit of a sequence...
متن کاملThe Urysohn, completely Hausdorff and completely regular axioms in $L$-fuzzy topological spaces
In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.
متن کامل