By using coverings we introduce the concepts of fibrewise covering uniform space and its generalizations (fibrewise generalized
uniform space and fibrewise semi-uniform space), and study the fibrewise completions of fibrewise generalized uniform spaces
and fibrewise semi-uniform spaces.
We introduce an alternative definition of fibrewise uniformity and discuss consequences deduced from new axioms. By modifying
James’ definition of fibrewise uniform structure, which is a slightly strengthened one, we define a new fibrewise uniformity
which is symmetric in global and realizes 1-1 correspondence between fibrewise entourage uniformities and fibrewise covering
uniformities. Moreover, we obtain a characterization of the fibrewise completion of fibrewise generalized uniform space as
a fibrewise extension of a fibrewise space. As an application of the fibrewise completion theory, we show that there exists
a fibrewise Shanin compactification of a fibrewise space.
Finally, we study extendability of fibrewise maps from dense subspaces. That is, for a fibrewise space X, A ⊂ X dense in X and a fibrewise continuous map f: A → Y, when can f be extended to the whole space X? Many characterization theorems of extendable fibrewise continuous maps are given.
Authors:M. Kubota, Y. Konami, H. Nakamura, and H. Amano
Macro-porous cation exchange resin Diaion CPK-08 and gel type cation exchange resin Dowex 50WX8 were irradiated with γ-rays
from60Co, while soaked in distilled water, 0.5M HNO3 or 4M HNO3, and the ion-exchange properties, such as strong- and weak-acid capacities, moisture content and wet resin volume, were examined
in relation to absorbed dose. There was no appreciable difference between the radiation stabilities of the two cation exchangers.
Increase of HNO3 concentration reduced the loss of strong-acid capacity and increased the decross-linkage and the weak-acid capacity. Elution
characteristics of137Cs and90Sr from columns packed with γ-irradiated resin were examined and the column distribution ratio of these radionuclides and
the theoretical plate number were calculated. These values decreased with the increase of absorbed dose. Diaion CPK-08 was
packed into a pressurized column and irradiated with γ-rays at a dose rate of 2·106 R/hr, while water was passed through the column at a constant flow rate. The greatest change of the resin properties was
observed at an upper stream position from the position of the highest radiation dose of 2·106 R/hr.