Fréchet-urysohn for Finite Sets
نویسندگان
چکیده
E. Reznichenko and O. Sipacheva called a space X “FréchetUrysohn for finite sets” if the following holds for each point x ∈ X: whenever P is a collection of finite subsets of X such that every neighborhood of x contains a member of P , then P contains a subfamily that converges to x. We continue their study of this property. We also look at analogous notions obtained by restricting to collections P of bounded size, we discuss connections with topological groups, the αi-properties of A.V. Arhangel’skii, and with a certain topological game.
منابع مشابه
Fixed Point Theory in Fréchet Spaces for Mönch Inward and Contractive Urysohn Type Operators
We present new fixed point theorems for inward and weakly inward Urysohn type maps. Also we discuss Mönch Kakutani and contractive type maps.
متن کاملProducts of Fréchet Spaces
We give a survey of results and concepts related to certain problems on the Fréchet-Urysohn property in products. This material was presented in a workshop at the 2005 Summer Conference on Topology and its Applications at Denison University.
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 کاملFurther Thoughts on Definability in the Urysohn Sphere
We discuss some basic geometry of sets definable in the Urysohn sphere using only finitely many parameters and briefly remark on the case of arbitrary definable sets. Then we discuss definable functions in the Urysohn sphere satisfying a special syntactic property.
متن کاملOn Quadratic Integral Equations of Urysohn Type in Fréchet Spaces
0 u(t, s, x(s)) ds, t ∈ J := [0,+∞), where f : J → R, u : J × [0, T ] × R → R are given functions and A : C(J,R) → C(J,R) is an appropriate operator. Here C(J,R) denotes the space of continuous functions x : J → R. Integral equations arise naturally from many applications in describing numerous real world problems, see, for instance, books by Agarwal et al. [1], Agarwal and O’Regan [2], Cordune...
متن کامل