scholarly journals Existence of Equilibria for Discontinuous Games in General Topological Spaces with Binary Relations

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ji-Cheng Hou
Keyword(s):  
Topological Spaces ◽  
Discontinuous Games ◽  
Binary Relations ◽  
Preference Relations ◽  
Convexity Structure ◽  
Existence Of Equilibria

We provide several results on the existence of equilibria for discontinuous games in general topological spaces without any convexity structure. All of the theorems yielding existence of equilibria here are stated in terms of the player’s preference relations over joint strategies.

scholarly journals Some consequence relations on propositional formulas

2011 ◽  
Vol 8 (1) ◽  
pp. 9-15
Author(s):  
Momcilo Borovcanin
Keyword(s):  
Risk Assessment ◽  
Decision Making ◽  
Consequence Relations ◽  
Binary Relations ◽  
Preference Relations ◽  
Short Overview ◽  
Logical Equivalence ◽  
Logical Entailment ◽  
Automated Decision Making ◽  
Product Control

Consequence relations on propositional formulas are binary relations on propositional formulas that represent certain types of entailment - formal or semi-formal derivation of conclusion from a certain set of premises. Some of well known examples are classical implication (standard logical entailment), preference relations (i.e. relations that satisfy Reflexivity, Left logical equivalence, Right weakening, And, Or and Cautious monotonicity) rational relations (i.e. preference relations that also satisfy rational monotonicity), consequence relations (prime examples are qualitative possibilities and necessities) etc. More than two decades various consequence relations are used in automated decision making, product control, risk assessment and so on. The aim of this paper is to give a short overview of the most prominent examples of consequence relations.

scholarly journals A generalization of Tong's theorem and properties of pairwise perfectly normal spaces

1985 ◽  
Vol 39 (3) ◽  
pp. 353-359
Author(s):  
Manuel López-Pellicer ◽  
Angel Gutiérrez
Keyword(s):  
Topological Spaces ◽  
Binary Relations ◽  
Closed Set ◽  
Perfect Normality ◽  
Semicontinuous Functions ◽  
Perfectly Normal

AbstractIn this paper we give some properties of the pairwise perfectly normal spaces defined by Lane. In particular we prove that a space (X, P, Q) is pairwise perfectly normal if and only if every P(Q)–closed set is the zero of a P(Q)–l.s.c. and Q(P)–u.s.c. function. Also we characterize the pairwise perfect normality in terms of sequences of semicontinuous functions by means of a result which contains the known Tong's characterization of perfectly normal topological spaces, whose proof we modify by using the technique of binary relations.

Concerning Binary Relations on Connected Ordered Spaces

1959 ◽  
Vol 11 ◽  
pp. 107-111 ◽  
Author(s):  
I. S. Krule
Keyword(s):  
Topological Semigroup ◽  
Unit Interval ◽  
General Nature ◽  
Topological Spaces ◽  
Binary Relations ◽  
Real Numbers ◽  
Topological Semigroups ◽  
Ordered Space

In a recent paper Mostert and Shields (4) showed that if a space homeomorphic to the non-negative real numbers is a certain type of topological semigroup, then the semigroup must be that of the non-negative real numbers with the usual multiplication. Somewhat earlier Faucett (2) showed that if a compact connected ordered space is a suitably restricted topological semigroup, then it must be both topologically and algebraically the same as the unit interval of real numbers with its usual multiplication.In studying certain binary relations on topological spaces there have become known (see, in particular, Wallace (5) and the author (3)) a number of properties analogous to those possessed by topological semigroups. Because of these analogous properties between relations and semigroups the author was motivated by the general nature of the Faucett and Mostert-Shields results (that is, that the multiplication assumed turned out to be the same as the usual multiplication) to feel that certain relations on a connected ordered space should turn out to be the same as the orders whose order topologies are the topology on the space.

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