Geodesic
On the Connectedness of the Sets of Limit Points of Certain Transforms of Bounded Sequences(1)
Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 175-181

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The transforms discussed here are the quasi-Hausdorff (Theorem 1), the [J, ƒ(x)] (Theorem 2) and the Borel integral means (Theorem 3). We are concerned here with whether or not the limit-points of these transforms of bounded sequences form connected sets. Such a set is one which cannot be decomposed into the union of two disjoint nonempty open sets. 
Leviatan, Dany; Lorch, Lee. On the Connectedness of the Sets of Limit Points of Certain Transforms of Bounded Sequences(1). Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 175-181. doi: 10.4153/CMB-1971-032-0
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     author = {Leviatan, Dany and Lorch, Lee},
     title = {On the {Connectedness} of the {Sets} of {Limit} {Points} of {Certain} {Transforms} of {Bounded} {Sequences(1)}},
     journal = {Canadian mathematical bulletin},
     pages = {175--181},
     year = {1971},
     volume = {14},
     number = {2},
     doi = {10.4153/CMB-1971-032-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-032-0/}
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