Vector Topology Research Articles

Gene Targeting Constructs: Effects of Vector Topology on Co-expression Efficiency of Positive and Negative Selectable Marker Genes

Targeting of DNA into specific chromosomal loci often involves the use of a negative selectable marker gene to enrich for cell clones that have undergone homologous recombination. In this study we asked if the arrangement of the positive and negative markers in ′knockout′ constructs can influence the expression of a lacZ gene that was used as a negative marker. We show that constructs which differ only in their topology have vastly different co-expression efficiencies. The site of DNA linearization was critical. While linearizing at the 5′-end of the lacZ gene was compatible with efficient lacZ expression, linearizing at the 3′-end was always detrimental. We also demonstrate that the topology of the template was more important than the promoter used to drive lacZ expression.

Separation of fuzzy normed linear spaces

This paper deals with Hausdorff separation axiom for fuzzy topological spaces. The necessary and sufficient condition obtained in the fuzzy vector topology induced by a fuzzy norm is separated. Properties of separated and non-separated fuzzy norms along with examples are studied. Separation of a fuzzy norm in terms of the ordinary norm it induces and its consequences are characterised. Separation of quotient fuzzy semi-norm is studied.

Effect of vector topology on homologous recombination at the CHO aprt locus.

The Chinese hamster ovary aprt gene was used as a model for studying the effect of vector topology on gene targeting frequency. A single recombination vector containing 2.7 kb of isogenic DNA homologous to the aprt gene was digested with eight separate restriction enzymes to generate a variety of both replacement- and insertion-type recombination substrates. The frequency of homologous recombination, normalized by cotransfection with a linearized neo' marker, was assayed by the correction of a mutant hemizygous aprt allele and was not found to reflect vector topology. Southern analysis of representative recombination products suggests that the gene targeting events occurred predominantly by double crossover/gene conversion.

Fuzzy topological vector spaces — topological generation and normability

Abstract Increasing awareness of the utility of fuzzy systems in modeling real life situations necessitates a thorough understanding of fuzzy topological vector spaces. In this paper, the first of several to follow on this topic, the generation of a fuzzy vector topology from an ordinary vector topology on a vector space is discussed. Also obtained is a condition for the fuzzy normability of a fuzzy vector topology induced by a family of fuzzy seminorms. Finally, an example indicating that the earlier mentioned condition is only sufficient is given.

Polynomials in topological vector spaces over valued fields

We consider the vector space of continuousm-homogeneous polynomials between topological vector spaces over a non-trivially valued field of characteristic zero and certain natural vector topologies on such spaces, and we prove polynomial versions of certain well known theorems of the linear theory of locally convex spaces.

Note on compatible vector topologies

Let ⟨ X , Y ⟩ \left \langle {X,Y} \right \rangle be a dual pair. Then X X admits the finest locally convex topology μ \mu which is compatible with ⟨ X , Y ⟩ \left \langle {X,Y} \right \rangle . In contrast, it is proved that there is no finest vector topology on X X which is compatible with ⟨ X , Y ⟩ \left \langle {X,Y} \right \rangle provided X X contains a μ \mu -dense subspace of infinite codimension.

A note on continuous dependence of solutions of Volterra integral equations

The topologies induced by two families of seminorms on a vector space of functions g: R + x R + x El -* El are compared. It is found that the continuous dependence of solutions of the Volterra equation x(t) f(t) + 5 , g(t, s, x(s)) ds does not hold for the weaker topology. This result corrects an error in the book of Miller, Benjamin, Menlo Park, Calif., 1971. The purpose of this paper is to give a counterexample to a proposition of R. K. Miller, concerning continuous dependence of solutions of Volterra integral equations. Consider the nonlinear Volterra equation x(t) = f(t) + f g(t, s, x(s)) ds, (E) where f E C(R +; E) (that is, f is a continuous function from R + = [0, oo) to the n-dimensional Euclidean space) and g is a function defined on R + X R + x En with values in En. In his book [2] Miller defines a vector space g of functions g: R + x R + x En--> En which satisfy certain hypotheses. Then he defines a family of seminorms on g (see (2) below) and proves, roughly speaking, that the solutions x of (E) depend continuously on the functionsf and g, where the functionsf belong to C(R +; En) topologized with the topology of uniform convergence on compact subsets and the functions g belong to 9 topologized with the locally convex vector topology induced by the seminorms mentioned above (cf. Theorem II.4.2 and its corollaries [2, pp. 108-116]). Miller gives an alternative characterization of the seminorms (see (4) below). In this note I will prove that this characterization is erroneous and that the seminorms on the right side of (4) lead to a topology on g for which the continuity theorems in [2] do not hold. The exact definition of g is given in [2, pp. 106-108]. For the purpose of this note it suffices to know that 9 contains all functions of the type g(t, s, x) = a(t s)h(s, x), (1) where h is a continuous function R + x En---En, and a is a locally integrable real valued function which vanishes on (oo, 0). The seminorms on 9 are defined in the following way (cf. [2, p. 107]): For every g E 9, every positive real number K and every bounded set B in Et, p(g, K, B) is defined by p(g, K, B) = sup{f Ig(t, s, p(s))I ds|t E[0, K], q E C([0, K]; B)}, (2) Received by the editors May 9, 1980. AMS (MOS) subject classifications (1970). Primary 45D05.

A Simplified Theory of the Scattering Geometries, Topologies and Vector Fields of Speckle Photography and Holographic Interferometry

In many applications of speckle photography or holographic interferometry to surface or structure distortion measurement some general understanding of the theory and optics of coherent light scattering from rough surfaces is important. In order to apply a simplified heuristic solution to the different flow patterns which occur with moving speckle patterns a geometrical optics method of diffraction, using diffractive rays, has been used. A modified initial model of this concept has associated the speckle movements with either (1) linear displacement of mirror facet sets on the scatter surface, or (2) rotations of tangent planes on the surface. A surface tangent free vector and cotangent axial vector system is developed, together with various lens and surface scattering geometries, and these are applied to the distorting surface using vector topology. Two topological flows are described, one for the surface in-plane free vector displacements, and the other for the axial vector rotations of the scatter surface; these speckle vector topologies are shown to be closely connected to the topographic scalar pathlength fringes of holographic interferometry.

A linearly compact convex set dense in every vector topology

A linearly compact convex set dense in every vector topology

Vector topologies and the representation of spaces of random variables

Most of the spaces of random variables are non-Hausdorff linear topological spaces, whereas a number of useful results of the theory of vector topologies require the Hausdorff separation axiom for the underlying spaces. Therefore we review and complete the machinery of non-Hausdorff linear topological spaces and the techniques for their representation with suitable Hausdorff linear topological spaces, and then we work out some examples, which emphasize the ideas involved in a consistent application of the topological point of view. The final part of the paper is devoted to the discussion of the pathology, which arises when we try to treat the special case of almost everywhere convergence in the same framework.

A Note on the Spaces L p for 0 < p 1

It is shown that there is no Hausdorff vector topology p on the space L (where 0 < p < 1) such that the unit ball of L is relatively compact for the topology p.

Vector topologies and linear maps on products of topological vector spaces

Vector topologies and linear maps on products of topological vector spaces

The nonstandard theory of topological vector spaces

The nonstandard theory of topological vector spaces

Metrics on test function spaces for canonical field operators

In a canonical field theory, the field Φ(f) and momentum π(g) are assumed defined for test functionsf andg which are elements of linear vector spaces and , respectively. Generally, the continuity of the map onto the unitary Weyl operatorsU(f),V(g) is taken as ray continuity, the barest minimum to recover the field operators as their generators, i.e.,U(f)=e iΦ(f) ,V(g)=e iπ(g) . This leaves open the question of whether any wider continuity properties follow and what form they would take. We show that much richer continuity properties do follow in a natural fashion for every cyclic representation of the canonical commutation relations. In particular, we show that the test function space may be taken as a metric space, that the space may be uniquely completed in this topology, and that the map into the unitary Weyl operators is strongly continuous in this topology. The topology induced by this metric is minimal in the sense that it is the weakest vector topology for which the mapsf→U(f),g→V(g) are strongly continuous. An expression for a suitable metric can easily be given in terms of a simple integral over a state on the Weyl operators.

Attempt at a Strongest Vector Topology

Attempt at a Strongest Vector Topology