We study geodesically complete and locally compact Hadamard spaces X whose Tits boundary is a connected irreducible spherical building. We show that X is symmetric iff complete geodesics in X do not branch and a Euclidean building otherwise. Furthermore, every boundary equivalence (cone topology homeomorphism preserving the Tits metric) between two such spaces is induced by a homothety. As an a...

Abstract Given a geometrically finite hyperbolic surface of infinite volume it is classical result Patterson that the positive Laplace–Beltrami operator has no $$L^2$$ L 2 -eigenvalues $$\ge 1/4$$ ≥ 1 / <mml:...

The notion of generalized locally bounded $I$-topological vectorspaces is introduced. Some of their important properties arestudied. The relationship between this kind of spaces and thelocally bounded $I$-topological vector spaces introduced by Wu andFang [Boundedness and locally bounded fuzzy topological vectorspaces, Fuzzy Math. 5 (4) (1985) 87$-$94] is discussed. Moreover, wealso use the fam...

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group N , there is a one-to-one correspondence between the set of isomorphism classes of connected Lie groups which are locally isomorphic to N and a union of certain quotients of noncompact Riemannian symmetric spaces.