Ishihara, H., Continuity properties in constructive mathematics. J. Symbolic Logic 57, pp. 557-565 (1992).  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... almost separating principle (ASP) and in the latter as weak limited principle of existence (WLPE) Under # Basic Research in Computer Science, funded by the Danish National Research Foundation. 1 the currently common name of weak Markov s principle it has been investigated by Ishihara ( 8] [9]) WMP plays a crucial role in the study of the interrelations between various continuity principles within the framework of Bishop style constructive mathematics ( 2] 3] 4] In order to state WMP we first need the notion of pseudo positivity : Definition 1 1) A real number a # IR is ....

Ishihara, H., Continuity properties in constructive mathematics. J. Symbolic Logic 57, pp. 557-565 (1992).

....we could prove constructively the standard versions of the inverse mapping theorem and the closed graph theorem. Troelstra [9] showed that in Brouwer s intuitionistic mathematics (INT) a sequentially continuous mapping on a separable metric space is continuous. On the other hand, Ishihara [6] [7] proved constructively that the continuity of sequentially continuous mappings on a separable metric space is equivalent to a certain boundedness principle for subsets of N; in the same paper, he showed that the latter principle holds within the recursive constructive mathematics (RUSS) of the ....

Hajime Ishihara, "Continuity properties in constructive mathematics", J. Symbolic Logic 57 (1992), 557-565.

....we could prove constructively the standard versions of the inverse mapping theorem and the closed graph theorem. Troelstra [9] showed that in Brouwer s intuitionistic mathematics (INT) a sequentially continuous mapping on a separable metric space is continuous. On the other hand, Ishihara [6] [7] proved constructively that the continuity of sequentially continuous mappings on a separable metric space is equivalent to a certain boundedness principle for subsets of N; in the same paper, he showed that the latter principle holds within the recursive constructive mathematics (RUSS) of the ....

Hajime Ishihara, "Continuity properties in constructive mathematics", J. Symbolic Logic 57 (1992), 557-565.

....2. 1 2 H. ISHIHARA AND R. MINES 1. Every nondiscontinuous function of a complete metric space into a metric space is sequentially continuous. 2. Every function of a complete metric space into a metric space is strongly extensional. 3. Every pseudopositive real number is positive. Ishihara [10] removed the assumption of the completeness of X , and showed that every sequentially continuous function from a separable metric space into a metric space is pointwise continuous if and only if every pseudobounded subset of N is bounded. Recently, Bridges and Mines [6] proved that a linear ....

....a is pseudopositive if it satis es 8x 2 R( 0 x) x a) We cannot show constructively that every pseudopositive real number is positive. This latter implication is weaker than MP, and is called Weak Markov Principle (WMP) See [9, 11] for an account of these two principles. Ishihara [10] called a countable subset A of N pseudobounded if lim n 1 an=n = 0 for all sequences fang in A, and used BD N to denote the statement If A is a pseudobounded countable subset of N, then A is bounded. 3. Strongly extensional and sequential continuity A mapping f between metric spaces is ....

H. Ishihara, Continuity properties in constructive mathematics, J. Symbolic Logic 57 (1992), 557-565.

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