Search results for "Topological vector space"
showing 10 items of 46 documents
On fuzzification of topological categories
2014
This paper shows that (L,M)-fuzzy topology of U. Hohle, T. Kubiak and A. Sostak is an instance of a general fuzzification procedure for topological categories, which amounts to the construction of a new topological category from a given one. This fuzzification procedure motivates a partial dualization of the machinery of tower extension of topological constructs of D. Zhang, thereby providing the procedure of tower extension of topological categories. With the help of this dualization, we arrive at the meta-mathematical result that the concept of (L,M)-fuzzy topology and the notion of approach space of R. Lowen are ''dual'' to each other.
TOPOLOGICAL PARTIAL *-ALGEBRAS: BASIC PROPERTIES AND EXAMPLES
1999
Let [Formula: see text] be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space [Formula: see text]. Then [Formula: see text] is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of [Formula: see text]. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of potential topological partial *-algebras, either function spaces (lattices of Lp spaces on [0, 1] or on ℝ, amalgam spaces), or partial *-algebras of operators (operators on a partial inner product space, O*-algebras).
Non absolutely convergent integrals of functions taking values in a locally convex space
2006
Properties of McShane and Kurzweil-Henstock integrable functions taking values in a locally convex space are considered and the relations with other integrals are studied. A convergence theorem for the Kurzweil-Henstock integral is given
Riemann type integrals for functions taking values in a locally convex space
2006
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Introduction to generalized topological spaces
2011
[EN] We introduce the notion of generalized topological space (gt-space). Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants) in terms of generalized spaces.
Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces
1993
In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Frechet spaces. We give an example of a Frechet-Schwartz space which is not the projective limit of a sequence of superreflex…
Banach spaces which are somewhat uniformly noncreasy
2003
AbstractWe consider a family of spaces wider than r-UNC spaces and we give some fixed point results in the setting of these spaces.
Injective spaces of real-valued functions with the baire property
1995
Generalizing the technique used by S.A. Argyros in [3], we give a lemma from which certain Banach spaces are shown to be non-injective. This is applied mainly to study the injectivity of spaces of real-valued Borel functions and functions with the Baire property on a topological space. The results obtained in this way do not follow from previous works about this matter.
On the structure of the ultradistributions of Beurling type
2008
Let O be a nonempty open set of the k-dimensional euclidean space Rk. In this paper, we give a structure theorem on the ultradistributions of Beurling type in O. Also, other structure results on certain ultradistributions are obtained, in terms of complex Borel measures in O.
Closedness and lower semicontinuity of positive sesquilinear forms
2009
The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.