ɪn mˌæθɪmˈæɾɪks, ðə pɑːɹtˈɪʃən təpˈɑːlədʒi ɪz ɐ təpˈɑːlədʒi ðæt kæn biː ɪndˈuːst ˌɔn ˌɛni sˈɛt baɪ pɑːɹtˈɪʃənɪŋ ˌɪntʊ dɪsdʒˈɔɪnt sˈʌbsɛts ðiːz sˈʌbsɛts fˈɔːɹm ðə bˈeɪsɪs fɚðə təpˈɑːlədʒi.
In mathematics, the partition topology is a topology that can be induced on any set  by partitioning  into disjoint subsets  these subsets form the basis for the topology.