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COUNTABLE AND UNCOUNTABLE

On generalized ω closed sets

On generalized ω closed sets

... Throughout this work, a space will always mean a topological space on which no separa- tion axiom is assumed unless explicitly stated. Let (X,τ) be a space and let A be a subset of X. A point x ∈ X is called a ...

11

Generating uncountable transformation semigroups

Generating uncountable transformation semigroups

... A Baire-0 function is just another name for a continuous function. A Baire-(n +1) function is a pointwise limit of Baire-n functions. It is not true in general that, for a fixed n, the set of Baire-n functions forms a ...

185

PP 2009 21: 
  Cofinality and Measurability of the First Three Uncountable Cardinals

PP 2009 21: Cofinality and Measurability of the First Three Uncountable Cardinals

... surability implies strong inaccessibility; they cannot be singular either, as successor cardinals are always regular. So, in ZFC, these three cardinals are non-measurable regular cardinals. But both of the mentioned ...

40

Amenability, Countable Equivalence Relations, and Their Full Groups

Amenability, Countable Equivalence Relations, and Their Full Groups

... The study of definable equivalence relations on standard Borel spaces in connection with different mathematical classification problems has been extensively pursued during the last two decades. The main notion that ...

97

Cichoń’s diagram for uncountable cardinals

Cichoń’s diagram for uncountable cardinals

... In this subsection, κ is always a – possibly weakly – inaccessible cardinal. The classical Cicho´ n diagram also contains cardinal invariants related to measure. While there are various attempts to generalize the ideal ...

44

Parity Objectives in Countable MDPs

Parity Objectives in Countable MDPs

... objectives in the following sections. In Section V we show that optimal strategies for B¨uchi objectives, where they exist, can be chosen MD, even for infinitely branching MDPs. In Section VI we consider finitely ...

11

CONFLICTS OF THE 21ST CENTURY BASED ON
MULTIDIMENSIONAL WARFARE– “HYBRID
WARFARE”, DISINFORMATION AND
MANIPULATION

CONFLICTS OF THE 21ST CENTURY BASED ON MULTIDIMENSIONAL WARFARE– “HYBRID WARFARE”, DISINFORMATION AND MANIPULATION

... is initiated from negative thoughts. The aspect of proper diagnosis is emphasised. “Know the enemy and know well each other, and in a hundred battles you will experience no disaster”. The elements of the art of war are ...

29

Assessing the Entropies of the Feigenbaum Strange Attractor and the S&P 500 Index as Factors Driving the Production of Information in Market Economies

Assessing the Entropies of the Feigenbaum Strange Attractor and the S&P 500 Index as Factors Driving the Production of Information in Market Economies

... Characteristics of SA vii Type: Strange viii Motion: Countable set of periodic orbits and uncountable set of aperiodic orbits ix SDIC: yes x Information Entropy: based on the time period[r] ...

12

Approaches for Helping Brazilian Students Improve their Scientific Writings

Approaches for Helping Brazilian Students Improve their Scientific Writings

... is countable, the most common choice is the article ...is uncountable, no article is used, as in “Our results show the necessity for Ø further research on this ...

5

A Theoretical Phenomenon Of Automorphism Of Groups

A Theoretical Phenomenon Of Automorphism Of Groups

... Hom(G/C,V), and in particular it is at most countable. On the other hand, as G/C and G are finite, the group G/U admits an infinite abelianhomomorphic image of exponent p, and so Hom(G/U, V) is ...

5

Probability Distributions.ppt

Probability Distributions.ppt

... • A continuous random variable is a variable that can assume any value on a continuum (can assume an uncountable number of values). – thickness of an item[r] ...

46

Compactness in Countable Fuzzy Topological Space 
                 

Compactness in Countable Fuzzy Topological Space  

... Proof: By the first part of the theorem 2.15, for a countable fuzzy topological space (X, C) to be fuzzy c- compact it is necessary that every c-open cover B of X has a finite 0-partition of X by B. That is, for ...

5

Lattices of topologies of algebraic systems

Lattices of topologies of algebraic systems

... 1) Ω contains a countable set I of coatoms such that elements of I are strongly incomparable (see [33]), hence (see Remark 2.4) Ω contains a sublattice isomorphic to the real line equipped with the natural order; ...

16

Variants of a lattice of partitions of a countable set

Variants of a lattice of partitions of a countable set

... Let M be a countable set. Let Part(M) be the set of all partitions of the set M. On the set Part(M) we can define a natural partial order. For any π 1 , π 2 ∈ Part(M) we say that π 1 6 π 2 if and only if from the ...

11

On Strong Determinacy of Countable Stochastic Games

On Strong Determinacy of Countable Stochastic Games

... TABLE I: Summary of determinacy and memory requirement properties for reachability, B¨uchi and Borel objectives and various probability thresholds. The results for safety and co-B¨uchi are implicit, e.g., > 0 B¨uchi ...

12

Universal sequences for the order automorphisms of the rationals

Universal sequences for the order automorphisms of the rationals

... In this paper, in the spirit of Galvin’s Theorem, we will show that Aut( Q , ≤) has a 2-letter universal sequence. In other words, every element from an ar- bitrary countable set can be given as a prescribed ...

25

Toward an ecological conception of timbre

Toward an ecological conception of timbre

... To conceive a new paradigm to sound parameters open uncountable perspectives to research on sonic manipulation techniques and consequently of musical composition (especially on comput[r] ...

12

A local approach to the entropy of countable fuzzy partitions

A local approach to the entropy of countable fuzzy partitions

... This paper generalizes the concept of entropy of fuzzy dynamical sys- tems in relation to countable partitions and examines its properties. The local entropy of a continuous dynamical system is finally proved to ...

8

Bayesian Entropy Estimation for Countable Discrete Distributions

Bayesian Entropy Estimation for Countable Discrete Distributions

... In a seminal paper, Nemenman and colleagues showed that for finite distributions with known A , Dirichlet priors with fixed a impose a narrow prior distribution over entropy (Nemenman et[r] ...

36

On weaker forms of compactness Lindelöfness and countable compactness

On weaker forms of compactness Lindelöfness and countable compactness

... pseudocompact, and an example of a space which is pseudocompact but not e-countably compact with respect to any dense set.. We also show that every e-.[r] ...

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