  The Steinitz exchange lemma is a basic theorem in linear algebra used, for
example, to show that any two bases for a finite-dimensional vector space have
the same number of elements. The result is named after the German mathematician
Ernst Steinitz. We present another proof of the result of N.J.S. Hughes
\cite{1} on Steinitz' exchange theorem for infinite bases. In our proof we
assume Kuratowski-Zorn Maximum Principle instead of well ordering. We present
some examples of dependence spaces of general nature with theirs possible
applications of the result in other as linear or universal algebra domains of
mathematical sciences. The lecture was presented on 77th Workshop on General
Algebra, 24th Conference for Young Algebraists in Potsdam (Germany) on 21st
March 2009.
