An Inverse System of Nonempty Objects with Empty Limit
In this article we give an explicit example of an inverse system with nonempty sets and onto bonding maps such that its inverse limit is empty.
math.CT↗
arXiv subjects
Veerendra Vikram Awasthi
Publications and source records attributed to Veerendra Vikram Awasthi.
Stone-Čech compactifications and homeomorphisms of products of the long line
In this note we shall prove that the Stone-Čech compactification of $\mathcal{L}^n$ is the space $\bar{\mathcal{L}}^n$ where $\bar{\mathcal{L}}$ is the extended long line, namely, $\mathcal{L}$ together with its ends $\pm Ω$. We give a similar description for the Stone-Čech compactification of the cartesian power of the semi-closed half-long line $\mathcal{L}_+$. As an application we show that any torsion subgroup of the group of all homeomorphisms of $\cj^n$ (resp. $\cl^n$) is isomorphic to a subgroup of the symmetric group $S_n$ (resp. the semidirect product $(\bz/2\bz)^n\ltimes S_n$).
math.GN↗