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Separation properties for self-conformal sets

Yuan-Ling Ye (2002)

Studia Mathematica

For a one-to-one self-conformal contractive system w j j = 1 m on d with attractor K and conformality dimension α, Peres et al. showed that the open set condition and strong open set condition are both equivalent to 0 < α ( K ) < . We give a simple proof of this result as well as discuss some further properties related to the separation condition.

Sequential continuity on dyadic compacta and topological groups

Aleksander V. Arhangel'skii, Winfried Just, Grzegorz Plebanek (1996)

Commentationes Mathematicae Universitatis Carolinae

We study conditions under which sequentially continuous functions on topological spaces and sequentially continuous homomorphisms of topological groups are continuous.

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