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About 1,034 papers for “Boolean spaces”

Boolean Functions Fitness Spaces

Langdon And Poli, W. B. Langdon, R. Poli · 1998

. We investigate the distribution of performance of the Boolean functions of 3 Boolean inputs (particularly that of the parity functions), the always-on-6 and even-6 parity functions. We use enumeration, uniform Monte-Carlo random sampling and sampling random full trees. As expected XOR dramatically changes the fitness distributions. In all cases once some minimum size threshold has been exceeded, the distribution of performance is approximately independent of program size. However the distribution of the performance of full trees is different from that of asymmetric trees and varies with tree depth. 1 Introduction Our investigations of the artificial ant following the Santa Fe trail [6] suggests that, provided programs are big enough, the distribution of program fitnesses is roughly independent of their size. That is if we pick a program of a certain size at random its as likely to perform as well as another program of a different size also chosen at random (provided both ex...

Cited by 0

Riesz spaces on Boolean rings

D. H. Fremlin · Cambridge University Press eBooks · 1974

The main purpose of this book is to show how the abstract theory of Riesz spaces may be applied to the study of function spaces arising in measure theory. In Chapters 1–3 I have set out the most important concepts needed for this approach. But in this chapter I propose to open up another line of attack. My eventual aim is to describe the relationship between the measure algebra of a measure space and its function spaces. In order to do this, I demonstrate methods of constructing Riesz spaces from Boolean algebras which, when applied to measure algebras, will produce isomorphic copies of the basic function spaces L1 and L∞. At the same time I shall apply the concepts of the first three chapters to describe the properties of these Riesz spaces.

Cited by 0

Boolean Images Of Connected Spaces

Al Safe, Arwa · UEA Digital Repository (University of East Anglia) · 2022

This thesis investigates an interesting generalisation of the concept of continuous functions, namely the notion of Boolean image. This type of image does not preserve connectedness, but otherwise has many of the properties of continuous images. We analyse this notion on many different kinds of topological spaces, deepening our understanding of combinatorial methods from set theory. The main contributions of this thesis can be summarized as follows. In chapter 3, we prove that every compact subspace of 2k with a finite support is a Boolean image of a connected space. This main result is followed by some applications in chapters 4 and 5 to different spaces, such as Eberlein compact spaces and Radon-Nikodým spaces, respectively. Chapter 6 centres around the connection between Banach spaces of continuous functions C(K) and C(L), in the case that the spaces L and K are both compact and zero-dimensional. In particular, we prove that if L is a a bijective Boolean image of a compact zero-dimensional space K, then C(L) is isometric to C(K). Moreover, we prove that if L is a Boolean image of K, then C(L) is isometric to a subspace of C(K). On the other hand, we prove that if the Banach spaces C(K) and C(L) are isomorphic, where the spaces K and L are zero-dimensional, then there is a subspace K′ in K and a subspace L′ in L such that K′ is a Boolean image of L′. In chapter 7, we examine some cardinal functions in terms of the possibility of being transferred via a Boolean image. In this respect, we show that weight and countable density are preserved by Boolean images.

Cited by 0

Majority Merging: from Boolean Spaces to Affine Spaces

Jean-François Condotta, Souhila Kaci, Pierre Marquis et al. · Frontiers in artificial intelligence and applications · 2010

This paper is centered on the problem of merging (possibly conflicting) information coming from different sources. Though this problem has attracted much attention in propositional settings, propositional languages remain typically not expressive enough for a number of applications, especially when spatial information must be dealt with. In order to fill the gap, we consider a (limited) first-order logical setting, expressive enough for representing and reasoning about information modeled as half-spaces from metric affine spaces. In this setting, we define a family of distance-based majority merging operators which includes the propositional majority operator ΔdH,Σ. We identify a subclass of interpretations of our representation language for which the result of the merging process can be computed and expressed as a formula.

Cited by 3

Boolean Valued Analysis of Banach Spaces

A. G. Kusraev, S. S. Kutateladze · Siberian Mathematical Journal · 2024

We implement the Boolean valued analysis of Banach spaces. The realizations of Banach spaces in a Boolean valued universe are lattice normed spaces. We present the basic techniques of studying these objects as well as the Boolean valued approach to injective Banach lattices.

Cited by 2

Sheaves of Algebras over Boolean Spaces

Arthur Knoebel · Birkhäuser Boston eBooks · 2011

Sheaves of Algebras over Boolean Spaces comprehensively covers sheaf theory as applied to universal algebra. The text presents intuitive ideas from topology such as the notion of metric space and the

Cited by 14Open access

Some notes concerning the homogeneity of Boolean algebras and Boolean spaces

Stefan Geschke, Saharon Shelah · ArXiv.org · 2002

We consider homogeneity properties of Boolean algebras that have nonprincipal ultrafilters which are countably generated.It is shown that a Boolean algebra B is homogeneous if it is the union of countably generated nonprincipal ultrafilters and has a dense subset D such that for every a in D the relative algebra B restriction a:= {b in B:b <= a} is isomorphic to B. In particular, the free product of countably many copies of an atomic Boolean algebra is homogeneous. Moreover, a Boolean algebra B is homogeneous if it satisfies the following conditions: (i) B has a countably generated ultrafilter, (ii) B is not c.c.c., and (iii) for every a in B setminus {0} there are finitely many automorphisms h_1, ...,h_n of B such that 1=h_1(a) cup ... cup h_n(a).

Cited by 0Open access

BOOLEAN FUNCTIONS: DIFFERENTIABLE MANIFOLDS AND AFFINE SPACES

Lucrarile Conferintei, Nationale De, Serban E. Vlad · 2015

The Boolean affine applications are the Boolean differentiable applications. If we accept to define the differentiable manifolds by replacing the differentiable structure with some atlas, then the affine spaces are special cases of differentiable manifolds. 0. Preliminaries (0.1) Definition},,1,0{2 ×Å=B is the field of the binary numbers, where ' ' Å is the modulo 2 sum and ' ' × is the intersection. It has the rough topology. (0.2) Definition The functions ': LLf ® , where ', LL are Boolean linear spaces, are called Boolean applications. From now on, we shall drop the attribute ’Boolean whenever possible. (0.3) Remark L becomes an affine space together with the function LyxxyxyyxyxLL def ÎÅ===' ´)()(), ( a where LLyx ®:, are translations. (0.4) Definition The affine applications f are these that satisfy: Lxxk k Î"Î " +121,...,,N,)(...)()... ( 121121 ++ ÅÅ=ÅÅ kk xfxfxxf (0.5) Definition If}| { Iiei Î is a base of L, then the first order derivatives of f are: Iixfexfxf ii ÎÅÅ= ¶),()()(

Cited by 0

Sums of Boolean spaces represent every group

Jiřı́ Adámek, Vácłav Koubek, Věra Trnková · Pacific Journal of Mathematics · 1975

For every Abelian group (S, +) there exist Boolean -i.e., compact, O-dimensional -topological spaces X s , se S f such that s + t = u if and only if X u is homeomorphic to the disjoint union of X, and X t . The method of the proof of this theorem is topological, utilizing mostly properties of Cech-Stone compactifications of various spaces. A corollary, obtained from well-known dualities, is the representability of Abelian groups (in an analogous sense) by products of rings, lattices, Boolean algebras, Banach spaces or Banach algebras.

Cited by 46Open access