Is sum of two decreasing convergent sequence to 0, a decreasing convergent sequence to 0 in Archimedean Riesz space?

Is sum of two decreasing convergent sequence to 0, a decreasing convergent sequence to 0 in Archimedean Riesz space? If an and bn are o-convergent, is an+bn also o-convergent?

02 September 2022 4,094 2 View