scholarly journals Changes of signs in conditionally convergent series on a small set

2011 ◽  
Vol 24 (11) ◽  
pp. 1831-1834
Author(s):  
Teresa Bermúdez ◽  
Antonio Martinón
Keyword(s):  
Convergent Series ◽  
Small Set ◽  
Conditionally Convergent Series

scholarly journals Achievement sets and sum ranges with ideal supports

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4911-4922
Author(s):  
Jacek Marchwicki
Keyword(s):  
Convergent Series ◽  
Topological Properties ◽  
Real Numbers ◽  
Small Set ◽  
Conditionally Convergent Series

We introduce the notion of ideally supported achievement sets for a series of real numbers. We analize their complexity and topological properties. We compare the notion of ideal achievement sets with the notion of ideally supported sum range of real series, considered by Filip?w and Szuca. We complete Filip?w and Szuca characterization of ideal sum ranges, [R. Filip?w, P. Szuca, Rearrangement of conditionally convergent series on a small set, J. Math. Anal. Appl. 362 (2010), no. 1, 64-71.], and we obtain some generalization of Riemann?s Theorem.

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