We show that for U (1)-symmetric spacetimes on S 3 × R a constant of motion associated with the well known Geroch transformation, a functional K[h ij , π ij ], quadratic in gravitational momenta, is strictly positive in an open subset of the set of all U (1)-symmetric initial data, and therefore not weakly zero. The Mixmaster initial data appear to be on the boundary of that set. We calculate t...

The lattice cell in the i + 1 st row and j + 1 st column of the positive quadrant of the plane is denoted i; j. If is a partition of n + 1 , w e denote by =ij the diagram obtained by removing the cell i; j from the French Ferrers diagram of. We set =ij = det k x pj i y qj be the linear span of the partial derivatives of =ij. The bihomogeneity o f =ij and its alternating nature under the diagona...

The class of countably intersected families of sets is defined. For any such family we define a Banach space not containing l(N). Thus we obtain counterexamples to certain questions related to the heredity problem for W.C.G. Banach spaces. Among them we give a subspace of a W.C.G. Banach space not containing l(N) and not being itself a W.C.G. space. INTRODUCTION In the present paper we deal wit...

The purpose of this paper is to introduce the concepts of semi*-connected spaces, semi*-compact spaces and semi*-Lindelof spaces. We investigate their basic properties. We also discuss their relationship with already existing concepts. Mathematics Subject Classification: 54D05, 54D30.

The behavior of various types of noncompact covering properties such as paracompactness, metacompactness, subparacompactness, submetacompactness, etc., are studied under various types of fuzzy mappings such as open map, closed map, perfect map, etc. Moreover the concept of para-Lindelof space is introduced in L-topological spaces and its properties and behavior under maps are obtained.

As is well known the category of paracompact spaces is important in algebraic topology and the theory of fiber spaces. The following question arises naturally. If a space (Hausdorff space) B is paracompact, is the space of paths B1 (I = [0, l]), with, of course, the compact-open topology, also paracompact? The following simple example answers the question in the negative. Let X denote the set o...