Before revision:  It should be also mentioned that D. Filiporvi\'{c --convex modules in D. Filipovi\'{c, M. Kupper, N. Vogelpoth, Separation and duality in locally L^0--convex modules, J. Funct.
After revision:  Then, we make use of the advantage of the (\varepsilon,\lambda)--topology and grasp the local property of L^0 --convex modules in D. Filipovi\'{c, M. Kupper, N. Vogelpoth, Separation and duality in locally L^0--convex modules, J. Funct.