Some propositions equivalent to the continuum hypothesis

Some Propositions Equivalent to the Continuum Hypothesis

Let 8 denote the real line. If TQ& and r £ 8 , we set {t+r: / £ J H } = r [ r ] . In [ l ] we have proved these two theorems: (BK) Let S C S , T C 8 , S be at most enumerable and T be of first category. Then 8 contains a residual subset R such that SC\T\r\ is empty for every rÇzR. (BM) Let S C S , 2"C8, S be at most enumerable and T be of measure zero. Then 8 contains a subset R such that 8— Ri...

A Property of the Real Line Equivalent to the Continuum Hypothesis

extensions of some polynomial inequalities to the polar derivative

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Equivalent continuum analyses of jointed rockmass: Some case studies

The paper presents summary of the work carried out by the author on the modelling of jointed rock mass with some field applications. The equivalent continuum analyses approach presented attempts to use statistical relations, which are simple and obtained after analyzing a large data from the literature on laboratory test results of jointed rock masses. Systematic investigations were done includ...

The Continuum Hypothesis

The continuum hypotheses (CH) is one of the most central open problems in set theory, one that is important for both mathematical and philosophical reasons. The problem actually arose with the birth of set theory; indeed, in many respects it stimulated the birth of set theory. In 1874 Cantor had shown that there is a one-to-one correspondence between the natural numbers and the algebraic number...