When I-Cauchy nets in complete uniform spaces are I-convergent

AbstractIn this paper we continue our investigation of nets using ideals in line of our earlier work where we had studied I-Cauchy nets and asked when I-Cauchy nets in complete uniform spaces are I-convergent in line of a problem by Di Maio and Kočinac who asked in 2008 when statistically Cauchy sequences are statistically convergent in uniform spaces. To answer this, here we consider another type of Cauchy condition of nets, namely I⁎-Cauchy condition and examine its basic properties and in particular its relation with the concept of I-Cauchy nets. This helps us to give an answer to the above mentioned open question