scholarly journals Weak Pareto optimality of multiobjective problems in a locally convex linear topological space

1982 ◽  
Vol 38 (1) ◽  
pp. 149-150
Author(s):  
M. Minami
Keyword(s):  
Topological Space ◽  
Pareto Optimality ◽  
Linear Topological Space ◽  
Weak Pareto Optimality ◽  
Multiobjective Problems ◽  
Locally Convex

scholarly journals Fixed point theorems for condensing multivalued mappings on a locally convex topological space

1975 ◽  
Vol 12 (2) ◽  
pp. 161-170 ◽  
Author(s):  
E. Tarafdar ◽  
R. Výborný
Keyword(s):  
Fixed Point ◽  
Topological Space ◽  
Fixed Point Theorems ◽  
Linear Topological Space ◽  
General Definition ◽  
Multivalued Mappings ◽  
Locally Convex

A general definition for a measure of nonprecompactness for bounded subsets of a locally convex linear topological space is given. Fixed point theorems for condensing multivalued mappings have been proved. These fixed point theorems are further generalizations of Kakutani's fixed point theorems.

A Decomposition Theorem for m-Convex Sets in Rd

1976 ◽  
Vol 28 (5) ◽  
pp. 1051-1057
Author(s):  
Marilyn Breen
Keyword(s):  
Topological Space ◽  
Convex Sets ◽  
Decomposition Theorem ◽  
Linear Topological Space ◽  
Local Convexity ◽  
Line Segments ◽  
Local Nonconvexity ◽  
Locally Convex

Let S be a subset of some linear topological space. The set S is said to be m-convex, m ≧ 2, if and only if for every m-member subset of S, at least one of the line segments determined by these points lies in S. A point x in S is said to be a point of local convexity of S if and only if there is some neighborhood N of x such that if y, z Є N ⌒ S, then [y, z] ⊆ S. If S fails to be locally convex at some point a in S, then q is called a point of local nonconvexity (lnc point) of S.

A Generalization of the Mapping Degree

1974 ◽  
Vol 26 (5) ◽  
pp. 1109-1117 ◽  
Author(s):  
D. G. Bourgin
Keyword(s):  
Topological Space ◽  
Linear Topological Space ◽  
Dimensional Case ◽  
Lefschetz Number ◽  
Mapping Degree ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
Locally Convex

For the single-valued case the notion of degree has been given recent expression by papers of Dold [5] for the finite dimensional case, and by Leray-Schauder [8] for the locally convex linear topological space. Klee [7] has removed this restriction by use of shrinkable in place of convex neighborhoods with the central role filled by a form of (2.15) below. For set-valued maps a modern formulation is, for instance, to be found in Gorniewicz-Granas [6]. These contributions relate the degree to the Lefschetz number, and the set-valued maps are required to map points into acyclic sets; that is to say, into "swollen points".

Intersections of m-Convex Sets

1975 ◽  
Vol 27 (6) ◽  
pp. 1384-1391 ◽  
Author(s):  
Marilyn Breen
Keyword(s):  
Topological Space ◽  
Convex Sets ◽  
Linear Topological Space ◽  
Local Convexity ◽  
Line Segments ◽  
Local Nonconvexity ◽  
Locally Convex

Let S be a subset of some linear topological space. The set S is said to be m-convex, m ≧ 2, if and only if for every m-member subset of line segments determined by these points lies in S. A point x in S is called a point of local convexity of S if and only if there is some neighborhood N of x such that if y, z ∈ N⋂ S, then [y, z] ⊆ S. If S fails to be locally convex at some point q in S, then q is called a point of local nonconvexity (lnc point) of S.

scholarly journals A characterization of pre-near-standardness in locally convex linear topological spaces

1972 ◽  
Vol 6 (1) ◽  
pp. 107-115
Author(s):  
J.J.M. Chadwick ◽  
R.W. Cross
Keyword(s):  
Topological Space ◽  
Dual Space ◽  
Linear Topological Space ◽  
Topological Spaces ◽  
Locally Convex

Let X be a locally convex linear topological space. A point z in an ultralimit enlargement of X is pre-near-standard if and only it is finite and for every equicontinuous subset S′ of the dual space X′, a point z′ belongs to *S′ ∩ μσ(X′, X) (0) only if z′ (z) is infinitesimal.

An Abstract Concept of the Sum of a Numerical Series

1970 ◽  
Vol 22 (4) ◽  
pp. 863-874 ◽  
Author(s):  
William H. Ruckle
Keyword(s):  
Topological Space ◽  
Sequence Space ◽  
Dual Space ◽  
Linear Topological Space ◽  
Sequence Spaces ◽  
Abstract Concept ◽  
Numerical Series ◽  
Locally Convex ◽  
Theory Of Duality

Our aim in this paper, generally stated, is to formulate an abstract concept of the notion of the sum of a numerical series. More particularly, it is a study of the type of sequence space called “sum space”. The idea of sum space arose in connection with two distinct problems.1.1 The Köthe-Toeplitz dual of a sequence space T consists of all sequences t such that st ∈ l1 (absolutely summable sequences) for each s∈T. It is known that if cs or bs is used in place of l1, an analogous theory of duality for sequence spaces can be developed (cf. [2]). What other spaces of sequences can play a rôle analogous to l1? This problem is treated in [6].1.2. Let {xn, fn} be a complete biorthogonal sequence in (X, X*), where X is a locally convex linear topological space and X* is its topological dual space.

Sequential convergence in locally convex spaces

1968 ◽  
Vol 64 (2) ◽  
pp. 341-364 ◽  
Author(s):  
J. H. Webb
Keyword(s):  
Topological Space ◽  
Linear Topological Space ◽  
Locally Convex Spaces ◽  
Convex Topology ◽  
Sequential Convergence ◽  
Locally Convex Topology ◽  
Locally Convex ◽  
Convergent Sequences ◽  
Convex Spaces

AbstractGiven a locally convex Hausdorff linear topological space, we construct and examine the following topologies in the space:the finest locally convex topology with the same convergent sequences as the initial topology, andthe finest locally convex topology with the same precompact sets as the initial topology.

scholarly journals Geometric structure of absolute basis systems in a linear topological space

1962 ◽  
Vol 12 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Robert Fullerton
Keyword(s):  
Topological Space ◽  
Geometric Structure ◽  
Linear Topological Space ◽  
Absolute Basis
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