2021/12/03 by Singha, Manoranjan, Roy, Sima
#FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2112.02028
One point compactification is studied in the light of ideal of subsets of ℕ. I-proper map is introduced and showed that a continuous map can be extended continuously to the one point I-compactification if and only if the map is I-proper. Shrinking condition(C) introduced in this article plays an important role to study various properties of I-proper maps. It is seen that one point I-compactification of a topological space may fail to be Hausdorff but a class \I\ of ideals has been identified for which one point I-compactification coincides with the one point compactification if it is metrizable.