15 research outputs found
On (transfinite) small inductive dimension of products
Get PDFsummary:In this paper we study the behavior of the (transfinite) small inductive dimension on finite products of topological spaces. In particular we essentially improve Toulmin's estimation [T] of for Cartesian products
ON SUM AND PRODUCT THEOREMS FOR DIMENSION DIND
No full textAbstract. For dimension Dind introduced by A. Arhangel’skij (cf. [2]) we prove that Dind is finite iff the large inductive dimension Ind is finite. We also establish various sum and product theorems for Dind more strong than ones for Ind in [10]. 1
Transfinite dimensions <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mi mathvariant="normal">Ind</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:math>
No full textThroughoutthisnoteweshallconsideronlyseparablemetrizablespaces. By dimensionwemeanthecoveringdimension dim.
No full textofinfinite-dimensionalCantormanifold
