In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

The set C(G) of closed subgroups of a locally compact group G has a natural topology which makes it a compact space. This topology has been defined in various contexts by Vietoris, Chabauty, Fell, Thurston, Gromov, Grigorchuk, and many others. The purpose of the talk was to describe the space C(G) first for a few elementary examples, then for G the complex plane, in which case C(G) is a 4–spher...

We prove that the weakly damped nonlinear Schrödinger flow in L 2 (R) provides a dynamical system which possesses a global attractor. The proof relies on the continuity of the Schrödinger flow for the weak topology in L 2 (R).

We give a survey on L-invariants such as L-Betti numbers and Ltorsion taking an algebraic point of view. We discuss their basic definitions, properties and applications to problems arising in topology, geometry, group theory and K-theory.

Experimental and theoretical results suggest that, since proteins are energetically minimally frustrated, the native fold, or topology, plays a primary role in determining the structure of the transition state ensemble and on-pathway intermediate states in protein folding. Although the central role of native state topology in determining the folding mechanism is thought to be a quite general re...

We extend some topologies on the space of upper semicontinuous functions with compact support to those on that of general upper semicontinuous functions and see that graphical topology and modified L topology are the same. We then define random upper semicontinuous functions using their topological Borel field and finally give a Choquet theorem for random upper semicontinuous functions.

let  be a graded ring and  be a graded -module. we define a topology on graded prime spectrum  of the graded -module  which is analogous to that for , and investigate several properties of the topology.

A net (xγ)γ∈Γ in a locally solid Riesz space (X,τ) is said to be unbounded τ-convergent x if |xγ−x|∧u⟶τ0 for all u∈X+. We recall that there linear topology uτ on X such τ-convergence coincides with uτ-convergence. It turns out characterised as the weakest which τ order bounded subsets. this motivation we introduce, uniform lattice (L,u), uniformity u⁎ L u subsets of L. shown induced by (X,τ), t...

We derive new representations for the generalised Jacobian of a locally Lipschitz map between finite dimensional real Euclidean spaces as lower limit (i.e., inferior) classical derivative where it exists. The lead to significantly shorter proofs basic properties subgradient and including chain rule. establish that sequence maps converges given in L-topology—that is, weakest refinement sup norm ...

If J is a set and Xj are topological spaces for each j ∈ J , let X = ∏ j∈J Xj and let πj : X → Xj be the projection maps. A basis for the product topology on X are those sets of the form ⋂ j∈J0 π −1 j (Uj), where J0 is a finite subset of J and Uj is an open subset of Xj , j ∈ J0. Equivalently, the product topology is the initial topology for the projection maps πj : X → Xj , j ∈ J , i.e. the co...