We prove characterization and resolution theorems for compact spaces and metrizable spaces with respect to cohomological dimension modulo $p$.

This paper provides eigenfunction expansions associated with the stationary problems for elastic wave propagation in stratified media $R^{3}$. The eigenfunction expansion is given in terms of generalized eigenfunctions corresponding to incident, reflected, refracted and Stoneley waves.

We prove the unique existence of solutions to some mixed problem of hyperbolic parabolic coupled systems with Neumann boundary condition, and we investigate how the constant in the first energy estimate depends on the coefficients of the opertors.

We prove a unique existence theorem of classical solutions to some Neumann problem of linear hyperbolic-parabolic coupled systems with coefficients in Sobolev spaces and energy estimates are also obtained. This paper gives a preparation for solving some nonlinear hyperbolic-parabolic coupled system with Neumann boundary condition.

Let $X$ be a compact metric space and $Y$ a stratifiable space. By $C(X, Y)$, we denote the space of continuous maps from $X$ to $Y$ with the compact-open topology. In general, $C(X, Y)$ is not stratifiable. In this paper, we show that $C(X, Y)$ is stratifiable if $Y$ satisfies the condition given by Mizokami [Mi]. And we construct a stratifiable space $Y$ such that $C(X, Y)$ is not stratifiable even if $X$ is countable and compact.