Geodesic
Compact Sets without Converging Sequences in the Random Real Model
Acta mathematica Universitatis Comenianae, Tome 76 (2007) no. 2 
A. Dow; D. Fremlin. Compact Sets without Converging Sequences in the Random Real Model. Acta mathematica Universitatis Comenianae, Tome 76 (2007) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2007_76_2_a3/
@article{AMUC_2007_76_2_a3,
     author = {A. Dow and D. Fremlin},
     title = {Compact {Sets} without {Converging} {Sequences} in the {Random} {Real} {Model}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2007},
     volume = {76},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2007_76_2_a3/}
}
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Voir la notice de l'article provenant de la source Comenius University

It is shown that in the model obtained by adding any number of random reals to a model of CH, there is a compact Hausdorff space of weight w 1 which contains no non-trivial converging sequences. It is shown that for certain spaces with no converging sequences, the addition of random reals will not add any converging sequences.