Sifat Jarak pada Ruang Metrik
Abstrack: Metric space is a
non empty set which has a function of distance with some special properties.
Function of distance in this metric space can define a set diameter, the
distance from the point to the set, as well as the distance from the set to the
set. The purpose of this thesis is to find the relationship between the
diameter of the set, the distance from the point to the set and distance from
the set to the set in any metric space. The method used in the proof of the
case is the analytical method. Results obtained by such methods as follows, if (𝑋,𝜌) is a metric spaces, 𝐴
and 𝐵
are subsets of 𝑋, 𝑥∈𝑋 which 𝐴⊆𝐵,
then 𝑑𝑖𝑎𝑚(𝐴)≤
𝑑𝑖𝑎𝑚(𝐵),
𝑑𝑖𝑠𝑡(𝑥,𝐵)≤𝑑𝑖𝑠𝑡(𝑥,𝐴)≤𝑑𝑖𝑠𝑡(𝑥,𝐵)+𝑑𝑖𝑎𝑚(𝐵),
and 𝑑𝑖𝑠𝑡(𝐴,𝐵)≤𝑑𝑖𝑠𝑡(𝑥,𝐴)+𝑑𝑖𝑠𝑡(𝑥,𝐵).
Moreover, if 𝑎,𝑏∈𝑋,𝑆⊆𝑋,
and 𝑆≠∅, then 𝑑𝑖𝑠𝑡(𝑎,𝑆)≤𝜌(𝑎,𝑏)+𝑑𝑖𝑠𝑡(𝑏,𝑆)
and |𝑑𝑖𝑠𝑡(𝑎,𝑆)−𝑑𝑖𝑠𝑡(𝑏,𝑆)|≤𝜌(𝑎,𝑏)≤𝑑𝑖𝑠𝑡(𝑎,𝑆)+𝑑𝑖𝑠𝑡(𝑏,𝑆)+𝑑𝑖𝑎𝑚(𝑆).
Penulis: Siti Maisyaroh,
Eridani, Miswanto
Kode Jurnal: jpmatematikadd130071
