Topology in Lattices

Frink, Orrin

doi:10.2307/1990078

Cited by 55 publications

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“…In view of 3.9 we need only show here that multiplication THE MEASURE ALGEBRA OF A LOCALLY COMPACT SEMIGROUP 209 in G is continuous. This follows from Theorems 2 and 3 [1], which assert that the lattice P k =iG k , being distributive, is a topological lattice.…”

Section: The Banach-algebra ^-/ίF{g) Is Semi-simplementioning

confidence: 86%

“…The proof is completed by noting that a subbase for the closed sets in the interval topology for G o is the collection From this it follows that the interval topology of G is the relativized interval topology of G o . By Theorems 3 and 4 [1] the former is equal to the product topology of G = Pk=iG k , and is therefore a locally compact T 2 -topology (2.7 [14]), having G o as its one-point compactification. The proof that G o is totally disconnected uses again the nature of G as a product space and Ross' result 2.8 [14].…”

Section: The Banach-algebra ^-/ίF{g) Is Semi-simplementioning

confidence: 99%

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The measure algebra of a locally compact semigroup

Baartz¹

1967

Pacific J. Math.

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Section: The Banach-algebra ^-/ίF{g) Is Semi-simplementioning

confidence: 86%

Section: The Banach-algebra ^-/ίF{g) Is Semi-simplementioning

confidence: 99%

The measure algebra of a locally compact semigroup

Baartz¹

1967

Pacific J. Math.

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“…Recall that a net {Fi : i £ D} of multifunctions from X into Y converges pointwise to F [5], denoted by Fi F, if for each point x £ X the net {Fi(x) : i £ D} converges to F(x) with respect to both upper and lower topologies on Vo(Y). Obviously, continuous convergence defined above is a natural extension of the corresponding notion for single-valued functions in Frink [9], and it implies pointwise convergence. The following two fundamental lemmas are very important in the sequel.…”

Section: Introductionmentioning

confidence: 99%

“…We find that the concept of continuous convergence will enable us to compare these convergences. Thus, in Section 2, we extend in a natural way this concept from the case of single-valued functions (see [9]) to the case of multifunctions and establish some characterizations. In the next section, we compare continuous convergence with topological convergence and graph convergence.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of Convergences for Multifunctions

Cao¹,

Reilly²,

Vamanamurthy³

1997

Demonstratio Mathematica

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In this paper, we extend the concept of continuous convergence for singlevalued functions to multifunctions and compare it with topological convergence in points, topological convergence in graphs, quasiuniform convergence and almost quasiuniform convergence. Relationships among these kinds of convergences are established and some of results from [3], [9], [11] and [14] are generalized. IntroductionThe concept of convergence of functions is indispensable in both analysis and topology. The purpose of this paper is to compare several types of convergences for multifunctions which have appeared in recent years.Let X and Y be two topological spaces. A subset A of X is said to be a-paracompact

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Isotone Recursive Methods: The Case of Homogeneous Agents

Reffett

Handbook on Optimal Growth 1

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractOver the last decade, isotone recursive methods have provided uni…ed catalog of results on existence, characterization, and computation of Markovian Equilibrium Decision Processes (MEDPs) in in…-nite horizon economies where the second welfare theorem fails. Such economies include models with production nonconvexities, taxes, valued …at money, models with monopolistic competition, behavioral heterogeneity, and incomplete markets. In this paper, we survey this emerging class of methods. Our methods use a qualitative approach to economic equilibria …rst introduced in the work in operations research by Veinott and Topkis. As the methods emphasize the role of order, they are amenable for obtaining conditions for monotone comparison theorems on the space of economies. We are also able to describe monotone iterative procedures that provide the needed foundations for a theory of numerical solutions for MEDPs and stationary Markov equilibrium (SME). One interesting additional result of independent interest is we construct su¢ cient conditions for the existence of a new class of envelope theorems for nonconcave programming problems.Email addresses: Manjira.Datta@asu.edu, Kevin.Re¤ett@asu.edu. We are deeply indebted to Len Mirman and Olivier Morand for numerous lengthy discussions concerning many issues discussed in this survey. Many of the results presented in this paper were developed originally in some form during our joint work with Len and Olivier over the last …ve years. We dedicate this paper to Len Mirman on the occasion of his sixty-…fth birthday. Indeed, this paper would not have been written without Len's ongoing pioneering work on equilibrium growth under uncertainty. We also thank Elena Antoniadou, Hector Chade, John Coleman, Jeremy Greenwood, Seppo Heikkila, Ken Judd, Tom Krebs, Cuong Le Van, Robert Lucas, Jr., Jianjun Miao, Chris Shannon, John Stachurski, Yiannis Vailakis, Charles Van Marrewijk, Jean-Marie Viaene, Itzhak Zilcha, and especially Robert Becker and Manuel Santos for many helpful conversations over the past years. All mistakes remain our own.

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Topology in Lattices

Cited by 55 publications

References 0 publications

The measure algebra of a locally compact semigroup

The measure algebra of a locally compact semigroup

Comparison of Convergences for Multifunctions

Isotone Recursive Methods: The Case of Homogeneous Agents

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