Rad HAZU, Matematičke znanosti, Vol. 21 (2017), 179-203.

ON THE QUOTIENT SHAPES OF VECTORIAL SPACES

Nikica Uglešić

Abstract.   The quotient shapes of vectorial spaces are considered - algebraically and topologically, especially, of the normed spaces. In the algebraic case, all the shape classifications and the isomorphism classification coincide. However, in the general topological case and, especially, in the normed case, the quotient shape classifications are strictly coarser than the isomorphism classification.

2010 Mathematics Subject Classification.   Primary 54E99; Secondary 55P55.

Key words and phrases.   Concrete category, (quotient) shape, (topological, normed) vectorial space, (continuous) linear function, quotient (topological, normed) vectorial space, dimension, infinite cardinal.

DOI: https://doi.org/10.21857/mzvkptxze9

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