Components of first-countability and various kinds of pseudoopen mappings

Some new classes of pseudoopen continuous mappings are introduced. Using these, we provide some sufficient conditions for an image of a space under a pseudoopen continuous mapping to be first-countable, or for the mapping to be biquotient. In particular, we show that if a regular pseudocompact space Y is an image of a metric space X under a pseudoopen continuous almost S-mapping, then Y is first-countable. Among our main results are Theorems 2.5, 2.11, 2.12, 2.13, 2.14. See also Example 2.15, Corollary 2.7, and Theorem 2.18.