On Embeddings of Compacta in Euclidean Space

Embeddings of Surfaces in Euclidean Three-space

Embeddings of Locally Connected Compacta

Let A' be a ^-dimensional compactum and /: X -» M" a map into a piecewise linear n-manifold. n > k + 3. The main result of this paper asserts that if X is locally (2k ^-connected and / is (2k n + l)-connected, then / is homotopic to a CE equivalence. In particular, every ^--dimensional, /-connected, locally /--connected compactum is CE equivalent to a compact subset of R2*~r as long as r < k 3....

Embeddings and Immersions of Manifolds in Euclidean Space

The problem of computing the number of embeddings or immersions of a manifold in Euclidean space is treated from a different point of view than is usually taken. Also, a theorem dealing with the existence of an embedding of Mm in ä ¡s given. Introduction. This paper studies the existence and classification of differential immersions and embeddings of a differentiable manifold into Euclidean spa...

Tangent Bundle Embeddings of Manifolds in Euclidean Space

For a given n-dimensional manifold M we study the problem of finding the smallest integer N(M) such that M admits a smooth embedding in the Euclidean space R without intersecting tangent spaces. We use the Poincaré-Hopf index theorem to prove that N(S) = 4, and construct explicit examples to show that N(S) ≤ 3n + 3, where S denotes the n-sphere. Finally, for any closed manifold M, we show that ...

On the Quaternionic Curves in the Semi-Euclidean Space E_4_2

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.