Related papers: Semigroups of Local Homeomorphisms

This paper has been withdrawn by the author due to a crucial error in formula 4.12.r

This paper has been withdrawn because of serious errors.

This paper has been withdrawn by the authors; it will be incorporated into part I of the series (in preparation).

This paper has been withdrawn. A significantly revised version will be posted in the near future.

This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.

This paper has been withdrawn by the author due to an error in an inequality in the proof of Theorem 1.1.

This paper has been withdrawn by the author, due to possible counter-examples.

The paper is withdrawn due to mistakes in the proofs for Proposition 1.2 and Theorem 2.2.

The paper has been withdrawn.

This paper has been withdrawn.

This paper has been withdrawn.

The paper is withdrawn.

The paper has been withdrawn due to a crucial error in section 3.

Examples are given of tent maps $T$ for which there exist non-trivial sets $B \subset [0,1]$ such that $T:B \to B$ is a homeomorphism.

In this paper, by reviewing the concept of semicovering maps, we present some conditions under which a local homeomorphism becomes a semicovering map. We also obtain some conditions under which a local homeomorphism is a covering map.

This paper has been withdrawn by the author due to an error in the proof of Theorem 1.

This paper has been withdrawn by the author because there are some typos in proofs.

This paper has been withdrawn by the author due to incomplete interpretation for the results.

This paper has been withdrawn

This paper has been withdrawn by the author due to a critical error in the proof of Theorem 5.4 on which the proof of the main theorem on the non-simplenss was based.