乘积Riesz空间的性质(英文)

THE PROPERTIES OF THE PRODUCT RIESZ SPACES

设{E_i;i∈I}是一族Riesz空间并且E=∏_(i∈I)E_i是Riesz空间的乘积。本文得到了E与其每一个因子空间E_i之间关于连续性、完备性、收敛性和稠密性等性质的关系。

Let {E_i : i ∈ I} be a family of Riesz spaces and E = Π_(i∈I)E_i be the product of Riesz spaces. In this paper, we obtain some relations between E and each factor spaces E_i concerning con- tinuity, convergence, completeness and density.