Separable extensions of first countable spaces
For a one-to-one self-conformal contractive system on 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 . We give a simple proof of this result as well as discuss some further properties related to the separation condition.
We study conditions under which sequentially continuous functions on topological spaces and sequentially continuous homomorphisms of topological groups are continuous.