Maximal elements of condensing preference maps in locally convex Hausdorff spaces

1991 ◽  
Vol 12 (8) ◽  
pp. 741-744
Author(s):  
Ding Xie-ping
Keyword(s):  
Hausdorff Spaces ◽  
Maximal Elements ◽  
Locally Convex

scholarly journals Maximal elements and equilibria for u-majorised preferences

1994 ◽  
Vol 49 (1) ◽  
pp. 47-54 ◽  
Author(s):  
Kok-Keong Tan ◽  
Xian-Zhi Yuan
Keyword(s):  
Existence Theorem ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
Qualitative Game ◽  
New Type ◽  
General Existence ◽  
Locally Convex

The purpose of this note is to give a general existence theorem for maximal elements for a new type of preference correspondences which are u-majorised. As an application, an existence theorem of equilibria for a qualitative game is obtained in which the preferences are u-majorised with an arbitrary (countable or uncountable) set of players and without compactness assumption on their domains in Hausdorff locally convex topological vector spaces.

scholarly journals Maximal elements and equilibria of generalized games for𝒰-majorized and condensing correspondences

1999 ◽  
Vol 22 (1) ◽  
pp. 179-189 ◽  
Author(s):  
George Xian-Zhi Yuan ◽  
E. Tarafdar
Keyword(s):  
Existence Theorem ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
New Type ◽  
Generalized Games ◽  
Locally Convex ◽  
Qualitative Games

In this paper, we first give an existence theorem of maximal elements for a new type of preference correspondences which are𝒰-majorized. Then some existence theorems for compact (resp., non-compact) qualitative games and generalized games in which the constraint or preference correspondences are𝒰-majorized (resp.,Ψ-condensing) are obtained in locally convex topological vector spaces.

Precompact linear operators in locally convex spaces

1957 ◽  
Vol 53 (3) ◽  
pp. 581-591 ◽  
Author(s):  
J. R. Ringrose
Keyword(s):  
Hausdorff Space ◽  
General Setting ◽  
Linear Operators ◽  
Fredholm Alternative ◽  
Locally Convex Spaces ◽  
Hausdorff Spaces ◽  
Alternative Theorem ◽  
Image Position ◽  
Complex Number Field ◽  
Locally Convex

This paper is concerned with the properties of precompact and compact linear operators from a locally convex Hausdorff space into itself, the field of scalars being the complex number field.The Riesz–Schauder theory for the equationswhere T is a compact linear operator from the Bacach space into itself, is well known (see, for example, Banach(1), Chapter 10, §2) and has been extended to the more general setting of locally convx Hausdorff spaces by Leray (4). In particular, the ‘Fredholm alternative theorem’ remains valid.

scholarly journals On strong lifting compactness, with applications to topological vector spaces

1986 ◽  
Vol 41 (2) ◽  
pp. 211-223 ◽  
Author(s):  
A. G. A. G. Babiker ◽  
G. Heller ◽  
W. Strauss
Keyword(s):  
Structural Properties ◽  
Weak Topology ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Hausdorff Spaces ◽  
Topological Vector Spaces ◽  
Completely Regular ◽  
Locally Convex ◽  
Convex Spaces

AbstractThe notion of strong lifting compactness is introduced for completely regular Hausdorff spaces, and its structural properties, as well as its relationship to the strong lifting, to measure compactness, and to lifting compactness, are discussed. For metrizable locally convex spaces under their weak topology, strong lifting compactness is characterized by a list of conditions which are either measure theoretical or topological in their nature, and from which it can be seen that strong lifting compactness is the strong counterpart of measure compactness in that case.

scholarly journals Notes on differential calculus in topological linear spaces, III

1976 ◽  
Vol 21 (1) ◽  
pp. 88-95
Author(s):  
S. Yamamuro
Keyword(s):  
Real Number ◽  
Number Field ◽  
Open Subset ◽  
Differential Calculus ◽  
Hausdorff Spaces ◽  
Real Numbers ◽  
Linear Spaces ◽  
Topological Linear ◽  
Locally Convex ◽  
Real Number Field

Throughout this note, let E, F and G be locally convex Hausdorff spaces over the real number field R. We denote real numbers by Greek letters. The sets of all continuous semi-norms on E and F will be denoted by P(E) and P(F) respectively, and A will always stand for an open subset of E.

scholarly journals A coincidence theorem in topological vector spaces

1986 ◽  
Vol 33 (3) ◽  
pp. 373-382 ◽  
Author(s):  
Olga Hadžić
Keyword(s):  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
Coincidence Theorem ◽  
Locally Convex ◽  
Special Case

In this paper we prove a coincidence theorem in not necessarily locally convex topological vector spaces, which contains, as a special case, a coincidence theorem proved by Felix Browder. As an application, a result about the existence of maximal elements is obtained.

Notes on differential calculus in topological linear spaces, II

1975 ◽  
Vol 20 (2) ◽  
pp. 245-252 ◽  
Author(s):  
S. Yamamuro
Keyword(s):  
Real Number ◽  
Number Field ◽  
Open Subset ◽  
Differential Calculus ◽  
Hausdorff Spaces ◽  
Real Numbers ◽  
Linear Spaces ◽  
Topological Linear ◽  
Locally Convex ◽  
Real Number Field

Throughout this note, let E and F be locally convex Hausdorff spaces over the real number field R. We denote real numbers by Greek letters. The sets of all continuous semi-norms on E and F will be denoted by P(E) and P(F) respectively, and A will always stand for an open subset of E.

Sign in / Sign up

Export Citation Format

Share Document