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

2017
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Filomat
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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,

doi:10.2298/fil1719165h
fatcat:cziqttfhvnh4vata7z4efk3yju