Countable product of function spaces having p-Frechet-Urysohn like properties

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Metrizability and the Frechet-Urysohn Property in Topological Groups

Weakly Continuously Urysohn Spaces

We study weakly continuously Urysohn spaces, which were introduced in [Z]. We show that every weakly continuously Urysohn w∆-space has a base of countable order, that separable weakly continuously Urysohn spaces are submetrizable, hence continuously Urysohn, that monontonically normal weakly continuously Urysohn spaces are hereditarily paracompact, and that no linear extension of any uncountabl...

Central subsets of Urysohn universal spaces

A subset A of a metric space (X, d) is central iff for every Katětov map f : X → R upper bounded by the diameter of X and any finite subset B of X there is x ∈ X such that f(a) = d(x, a) for each a ∈ A ∪ B. Central subsets of the Urysohn universal space U (see introduction) are studied. It is proved that a metric space X is isometrically embeddable into U as a central set iff X has the collinea...

Partitions and indivisibility properties of countable dimensional vector spaces

8 We investigate infinite versions of vector and affine space partition 9 results, and thus obtain examples and a counterexample for a parti10 tion problem for relational structures. In particular we provide two 11 (related) examples of an age indivisible relational structure which is 12 not weakly indivisible. 13