Sequence-covering and countably bi-quotient mappings

Onk-quotient mappings

“…Thus the direct compact analogy of Theorem 5.4 in [5], which would be Y is a //-space if and only if every kquotient mapping onto Y is preudo-open, is false. This example also shows that Theorem 4.6 of [9] and 2.4 of [10] can not be improved by using //quotient mappings alone. In particular, it is false that if Y is a strongly //-space [9] then every //quotient mapping onto Y is countably bi-quotient, and it is false that if Y is locally compact then every //quotient mapping onto Y is bi-quotient.…”

“…3* Functional characterization of λ>sρaces and defining A> systems* In this section the theorems are either compactly generated analogies to theorems in [5], improvements of theorems in [9] or modifications of theorems in [3]. The notions of defining ^-systems and defining ^-systems of Arhangelskiϊ are fundamentally involved with the mappings of this paper.…”

I: Fréchet-Urysohn spaces

“…is an infinite subsequence of S. Equivalently, if whenever {y n } is a convergent sequence in Y , there is a convergent sequence {x k } in X with each x k ∈ f −1 (y n k ) [30]. Definition 1.3.…”

A countably compact 𝑘’-space need not be countably 𝑏𝑖-𝑘

“…Introduction. In recent years Arhangel'skiï [1], [2], Siwiec [10], and Michael [6] characterized images of certain kinds of spaces under certain kinds of mappings. These characterizations are summarized in Table 1 All the terms in this table are defined in [6].…”