A study of stable Hopf invariants and Hopf constructions

在框括号和矩阵户田括号之间得到公式。得到了户田经典公式的推广，包括与Hopf不变量的关系。定义了一类与LS范畴密切相关的空间。阐明了类空间和覆盖空间之间的关系，这对研究实例是有用的。研究了由指数拓扑定义的函数空间的拓扑。证明了指数同胚对任何拓扑空间都成立，并给出了该定理的应用。

Formulas are obtained among box brackets and matrix Toda brackets. Generalizations of classical formulas by Toda are obtained including relations with the Hopf invariants. A class of spaces is defined which is closely connected with the LS category. Relations between the class and covering spaces are clarified which are useful to study examples. Topologies of function spaces which are defined by the exponential topology are studied. Exponential homeomorphisms are proved which hold for any topological spaces and applications of the theorem are obtained.