We give some conditions ensuring that a light mapping $f:X\rightarrow Y$ between compacta must be injective on a non-trivial continuum and we discuss related questions concerning the invariance of strong infinite-dimensionality.

We associate to every holomorphic function of one complex variable a semi-symmetric hypersurface in the fourdimensional Euclidean space. Under simple explicit conditions for this function the resulting Riemannian space is complete and of hyperbolic type (in the terminology of Szabớ).

Let $M$ be an n-dimensional pseudo-umbilical submanifold in an $(n+p)$ -dimensional space form $N^{n+p}(C)$. In this paper, we obtain some generalizations of B. Y. Chen in [1].

Let $G(H)$ be the Chevalley (Steinberg) Kac-Moody group of the Kac-Moody Lie algebra $L$. If $\sigma$ is the canonical homomorphism of $H$ onto $G$, and $\{B_{G}, N_{G}\}$ is the Tits system in $G$, then $\{\sigma^{-1}(B_{G}),\sigma^{-1}(N_{G})\}$ is a Tits system in the Weyl-simple subgroup of $H$.

Using a Dennis-Stein symbol, we will study $K_{2}(2,Z[\frac{1}{p}])$ and the meta-abelianization of $SL(2,Z[\frac{1}{p}])$

In testing statistical hypotheses, quite generally, if we admit the result of Neyman-Pearson (apart from the interpretation of them) in case that we specify $n$ in advance and admit the likelihood principle, the stopping rule that “continue the experiments until rejecting the null hypothesis” is closed. As a matter of fact, a stronger phenomenon happens, and we shall show it with some examples.

We state some sum theorems for the strong small transfinite dimension in different classes of topological spaces.

Subject to certain faithfulness requirements in a morita context for near-rings, a canonical representation thereof is provided. Necessary and sufficient conditions (using an idempotent element) on a near-ring are given which determine when the nearring is a morita near-ring.

Let $R$ be a commutative ring with identity. The main result of the paper is the following: THEOREM. Let $f:Z\rightarrow X$ be a $UV^{n-1}$-mapping from a compactum $Z$ of dimension $\leq n$ onto a compactum $X$. If $H^{n}(f^{-1}(x);R)=0$ for all $x\in X$, then $a-dim_{R}X\leq n$. As its consequence, we have a characterization of compacta $X$ of $a-dim_{R}X\leq n$. THEOREM. A compactum $X$ admits a $UV^{n-1}$ -mapping $f:Z\rightarrow X$ from a compactum $Z$ of dimension $\leq n$ onto $X$ such that $H^{n}(f^{-1}(x);R)=0$ for all $x\in X$ if and only if $a-dim_{R}X\leq n$.

In this paper we shall give an introduction to the geometry of higher order Lagrange spaces. The gravitational field, Einstein equations, as well as the electromagnetic fields and generalized Maxwell equations, are pointed out, too.

We generalize Ejiri’s theorem about minimal submanifolds in warped product manifolds and see that there exist minimal immersions of the plane and the catenoid into other Riemannian manifolds.

We show, assuming analytic determinacy, that the hyperspace consisting of compact sets of rational numbers is topologically homogeneous.