The fixed point property of the smallest open neighborhood of the n-dimensional Khalimsky topological space

Sang-Eon Han
2017 Filomat  
The paper aims to propose the fixed point property(FPP for short) of smallest open neighborhoods of the n-dimensional Khalimsky space and further, the FPP of a Khalimsky (K-, for short) retract. Let (X, κ n X ) be an n-dimensional Khalimsky topological space induced by the n-dimensional Khalimsky space denoted by (Z n , κ n ). Although not every connected Khalimsky topological space (X, κ n X ) has the FPP, we prove that for every point x ∈ Z n the smallest open K-topological neighborhood of x,
more » ... denoted by SN K (x) ⊂ (Z n , κ n ), has the FPP. Besides, the present paper also studies the almost fixed point property (AFPP, for brevity) of a K-topological space. In this paper all spaces (X, κ n X ) := X are assumed to be connected and | X | ≥ 2.
doi:10.2298/fil1719165h fatcat:cziqttfhvnh4vata7z4efk3yju