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ISSN : 1226-0657

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Vol.2 No.1
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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1995, v.2 no.1, pp.43-51
Lee, Sang-Han
Lee,, S. (1995). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 2(1), 43-51.
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Abstract

In this paper, we introduce the almost linear spaces, a generalization of linear spaces. We prove that if the almost linear space X has a finite basis then, as in the case of a linear space, the cardinality of bases for the almost linear space X is unique. In the case X = Wx ＋ Vx, we prove that B'= {<TEX>$\chi$</TEX>'<TEX>$_1,...,x'_n</TEX>} is a basis for the algebraic dual X<TEX>$^#$</TEX> of X if B = {<TEX>$\chi$</TEX>'<TEX>$_1,...,x'_n</TEX>} is a basis for the almost linear space X. And we have an example X(<TEX>$\neq$</TEX>Wx ＋ Vx) which has no such a basis.

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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