Countable dense homogeneity property of connected compact manifolds

Main Article Content

Cinderella T.J.
Vinod Kumar P.B.

Abstract

Let X be a connected compact manifold and H(X) denote the set of all homeomorphisms from X onto itself. In this paper we provide another proof for the known result that every connected compact manifolds are n−homogeneous and thereby countable dense homogeneous (CDH). We also show that every compact manifold can be expressed as a disjoint union of countable dense subsets. Additionally, we prove that for every h ∈ H(X), a partition of X in to countable dense subsets on which it is invariant. Mainly, we discuss about the denseness of HA(X) = { h ∈ H(X) | h : A → A is a homeomorphism } in H(X) whenever A is a subset of X. Finally, we prove that if f is a contraction function on X, then the set of all homeomorphisms that commutes with f is a nowhere dense subgroup of H(X).

Downloads

Download data is not yet available.

Article Details

How to Cite
T.J., C., & P.B., V. K. (2024). Countable dense homogeneity property of connected compact manifolds. Gulf Journal of Mathematics, 17(2), 208-215. https://doi.org/10.56947/gjom.v17i2.2122
Section
Articles