Monotonically normal topological vector spaces are stratifiable

We prove that for any Hausdorff topological vector space E over the field R there exists A subset of E such that E is homeomorphic to a subset of A x R and A x R is homeomorphic to a subset of E. Using this fact we prove that E is monotonically normal if and only if E is stratifiable.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Universal Abelian topological groups

A topological group G is said to be universal in a class K of topological groups if G is an element of K and if for every group H is an element of K there is a subgroup K of G that is isomorphic to H as a topological group. A group is constructed that is universal in the class of separable metrizable topological Abelian groups.

A topological algorithm for identification of structural domains of proteins

Background: Identification of the structural domains of proteins is important for our understanding of the organizational principles and mechanisms of protein folding, and for insights into protein function and evolution. Algorithmic methods of dissecting protein of known structure into domains developed so far are based on an examination of multiple geometrical, physical and topological features. Successful as many of these approaches are, they employ a lot of heuristics, and it is not clear whether they illuminate any deep underlying principles of protein domain organization. Other well-performing domain dissection methods rely on comparative sequence analysis. These methods are applicable to sequences with known and unknown structure alike, and their success highlights a fundamental principle of protein modularity, but this does not directly improve our understanding of protein spatial structure.

Topological mappings between graphs, trees and generalized trees

We present novel topological mappings between graphs, trees and generalized trees that means between structured objects with different properties. The two major contributions of this paper are, first, to clarify the relation between graphs, trees and generalized trees, a graph class recently introduced. Second, these transformations provide a unique opportunity to transform structured objects into a representation that might be beneficial for a processing, e.g., by machine learning techniques for graph classification. (c) 2006 Elsevier Inc. All rights reserved.

Topological analysis of the Escherichia coli WcaJ protein reveals a new conserved configuration for the polyisoprenyl-phosphate hexose-1-phosphate transferase family

WcaJ is an Escherichia coli membrane enzyme catalysing the biosynthesis of undecaprenyl-diphosphate-glucose, the first step in the assembly of colanic acid exopolysaccharide. WcaJ belongs to a large family of polyisoprenyl-phosphate hexose-1-phosphate transferases (PHPTs) sharing a similar predicted topology consisting of an N-terminal domain containing four transmembrane helices (TMHs), a large central periplasmic loop, and a C-terminal domain containing the fifth TMH (TMH-V) and a cytosolic tail. However, the topology of PHPTs has not been experimentally validated. Here, we investigated the topology of WcaJ using a combination of LacZ/PhoA reporter fusions and sulfhydryl
labelling by PEGylation of novel cysteine residues introduced into a cysteine-less WcaJ. The results showed that the large central loop and the C-terminal tail both reside in the cytoplasm and are separated by TMH-V, which does not fully span the membrane, likely forming a "hairpin" structure. Modelling of TMH-V revealed that a highly conserved proline might contribute to a helix-break-helix structure in all PHPT members. Bioinformatic analyses show that all of these features are conserved in PHPT homologues from
Gram-negative and Gram-positive bacteria. Our data demonstrate a novel topological configuration for PHPTs, which is proposed as a signature for all members of this enzyme family