I've been studying the korovin functions for two days. There are 3 statements that I do not know because they are true and I hope you can help me. thanks for your help. First I give you the definition of function of korovin and the context where I am.
the statements that I do not understand because they are true are the ones that are highlighted and that I write below.
1) Why we can write $\mathcal{E} = \{f_α : \alpha < \mathfrak{c}\}$?
2) Why for $h_0=f_0$ the conditions 1) and 2) are trivially satisfied at the level? Here what is exactly the 0?
3) Why $|G_\beta|<\mathfrak{c}$? why it can not happen that $|G_\beta|=\mathfrak{c}$?
Thanks so much for your help!