Function spaces of CW homotopy type are Hilbert manifolds

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...

Compact Open Topology and Cw Homotopy Type

CW Type of Inverse Limits and Function Spaces

We continue the investigation of CW homotopy type of spaces of continuous functions between two CW complexes begun by J. Milnor in 1959 and P. Kahn in 1984. Viewing function spaces as particular cases of inverse limits we also study certain inverse systems of fibrations between CW homotopy type spaces. If the limit space Z∞ of an inverse sequence {Zi} of fibrations between CW type spaces has CW...

On the Rational Homotopy Type of Function Spaces

The main result of this paper is the construction of a minimal model for the function space F(X,Y ) of continuous functions from a finite type, finite dimensional space X to a finite type, nilpotent space Y in terms of minimal models for X and Y . For the component containing the constant map, π∗(F(X,Y ))⊗Q = π∗(Y ) ⊗ H−∗(X;Q) in positive dimensions. When X is formal, there is a simple formula ...

Detecting Hilbert Manifolds among Homogeneous Metric Spaces

We detect Hilbert manifolds among homogeneous metric spaces and apply the obtained results to recognizing Hilbert manifolds among homogeneous spaces of the form G/H where G is a metrizable topological group and H is a closed balanced subgroup of G.