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Factorization theorems in dimension theory

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CONTENTSIntroduction § 1. Factorization theorems and methods for obtaining them § 2. Applications of factorization theorems § 3. The dimension of topological productsReferences

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... If A is a normal space, since dimZ < dim A if Z is either closed or cozero in A, then loc dim X < « iff A has an open cover {GÁ : X e A} with dim Gx< « for each X in A, which is the original definition of loc dim [4]. Following [10], if /: A -» Y is continuous, by W(f) we denote the smallest cardinal a for which there exists a space Z of weight a and an embedding g : X -y Y x. Z with / = nog, where n denotes the canonical projection from Y x Z onto Y . ...
... The last result can be rephrased as follows. Recall that pwX is the supremum of all cardinals a for which there exists a map from A onto a metrizable space of weight a [10]. Proposition 13. ...
... y < « , and this completes the proof.For the rest of our results we need a lemma and a simplified version of[3, Theorem 9]. Recall that bwX is the smallest cardinal x for which there exists a continuous f:X-yM with M metrizable and W(f) = x[10].License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use ...
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CONTENTS Introduction § 1. Some auxiliary propositions § 2. Some auxiliary constructions in and “over” § 3. A theorem on - (and -) maps for maps into an -dimensional cube § 4. A theorem on -maps for maps of compact spaces § 5. A factorization theorem for maps § 6. A theorem on -maps for maps of bicompact spaces References
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