Dispersion points and continuous functions

Two countable, biconnected, not widely connected Hausdroff spaces

“…Biconnected spaces (countable or not, with or without a dispersion point) are considered in [26,37,1,2,3,4,6,9,10,11,18,19,21,22,25,27,28,29,33,38,39] and maximal connected spaces in [13,1,5,8,12,14,15,32,35].…”