Note on Weakly n -Dimensional Spaces | Zendy

Jan van Mill | Zendy; Roman Pol | Zendy

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Note on Weakly n -Dimensional Spaces

Author(s) -

Jan van Mill,

Roman Pol

Publication year - 2001

Publication title -

monatshefte für mathematik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 37

eISSN - 1436-5081

pISSN - 0026-9255

DOI - 10.1007/s006050170056

Subject(s) - mathematics , linear subspace , disjoint sets , countable set , class (philosophy) , cover (algebra) , pure mathematics , space (punctuation) , dimension (graph theory) , product (mathematics) , discrete mathematics , combinatorics , computer science , geometry , mechanical engineering , artificial intelligence , engineering , operating system

Weakly n-dimensional spaces were first distinguished by Karl Menger. In this note we shall discuss three topics concerning this class of spaces: universal spaces, products, and the sum theorem. We prove that there is a universal space for the class of all weakly n-dimensional spaces, present a simpler proof of Tomaszewski's result about the dimension of a product of weakly n-dimensional spaces, and show that there is an n-dimensional space which admits a pairwise disjoint countable closed cover by weakly n-dimensional subspaces but is not weakly n-dimensional itself

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