Note on % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBqj3BWbIqubWexLMBb50ujbqegm0B % 1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr % Ffpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0F % irpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaa % GcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvgaiuaacqWF % qessryqr1ngBPrgaiyGacqGFsbGuaaa!4796! $$ \mathcal{I}R $$ -closed and % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBqj3BWbIqubWexLMBb50ujbqegm0B % 1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr % Ffpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0F % irpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaa % GcbaGaamyqamaaBaaaleaatuuDJXwAK1uy0HwmaeXbfv3ySLgzG0uy % 0Hgip5wzaGqbaiab-brijfHbfv3ySLgzaGGbciab+jfasbqabaaaaa!4888! $$ A_{\mathcal{I}R} $$ -sets

Abstract

We characterize and discuss the properties of \( \mathcal{I}R \)-closed sets and \( A_{\mathcal{I}R} \)-sets. Also, we give characterizations of weakly \( \mathcal{I} \)-locally closed sets and \( \mathcal{I} \)-submaximal spaces. A characterization of codense ideals in terms of \( \mathcal{I}R \)-closed sets is also given.