J. Korean Math. Soc. 2013; 50(5): 933-944
Printed September 1, 2013
https://doi.org/10.4134/JKMS.2013.50.5.933
Copyright © The Korean Mathematical Society.
Xia Zhang
Tianjin Polytechnic University
Based on the four kinds of theoretical definitions of the continuous module homomorphism between random locally convex modules, we first show that among them there are only two essentially. Further, we prove that such two are identical if the family of $L^{0}$-seminorms for the former random locally convex module has the countable concatenation property, meantime we also provide a counterexample which shows that it is necessary to require the countable concatenation property.
Keywords: random locally convex modules, $(\varepsilon,\lambda)$-topology, locally $L^{0}$-convex topology, continuous module homomorphisms
MSC numbers: Primary 46H25, 46A03, 46E10
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