ðɪ ɪmpˈoːɹtənt fˈiːtʃɚz ʌv ðɪs sˈɛt ɑːɹ ðˌɐɾɪt ɪz kənˈɛktᵻd ænd pˈæθkənˈɛktᵻd ɪnðə juːklˈɪdiːən təpˈɑːlədʒi ɪn ænd ðɪ ˈɔːɹɪdʒˌɪn ɪz ɐ lˈɪmɪt pˈɔɪnt ʌvðə sˈɛt, ænd jˈɛt ðə sˈɛt ɪz θˈɪn æt ðɪ ˈɔːɹɪdʒˌɪn, æz dᵻfˈaɪnd ɪnðɪ ˈɑːɹɾɪkəl fˈaɪn təpˈɑːlədʒi pətˈɛnʃəl θˈiəɹi.
The important features of this set are that it is connected and path-connected in the euclidean topology in  and the origin is a limit point of the set, and yet the set is thin at the origin, as defined in the article Fine topology (potential theory).