CONTENTS 1. Introduction........................................................................................................................................................................... 5 2. Countably bi-quotient maps and their two generalizations......................................................................................... 9 3. Relatively pseudocompact and lightly compact subsets............................................................................................ 12 4. A'-spaces.............................................................................................................................................................................. 13 5. Internal characterizations and implications for A-spaces and A'-spaces................................................................ 15 6. Characterizations of the mapping properties in Diagram 1.2 and of one other mapping property.................... 20 7. Proofs for Diagram 1.2 and Corollary 1.4....................................................................................................................... 24 8. Proofs for Diagram 1.3....................................................................................................................................................... 25 9. Operations which preserve various kinds of A-spaces and A'-spaces.................................................................... 26 10. A modification of single A-spaces................................................................................................................................. 29 11. Examples........................................................................................................................................................................... 32 References............................................................................................................................................................................... 43
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