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A-spaces and countably bi-quotient maps

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Rozprawy Matematyczne tom/nr w serii: 133 wydano: 1976
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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
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 133
Liczba stron
43
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXXXIII
Daty
wydano
1976
Twórcy
autor
autor
autor
Bibliografia
  • [1] K. Alster, Remarks on compact-covering mappings, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys. 19 (1971), pp. 141-148.
  • [2] A. V. Arhangel'skii, Mappings and spaces, Uspehi Mat. Nauk 21 (1966), pp. 133-184 (= Russian Math. Surveys 21 (1966), pp. 115-162).
  • [3] A. V. Arhangel'skii, The frequency spectrum of a topological space and the classification of spaces, Dokl. Akad. Nauk SSSR 206 (1972), pp. 265-268 (= Soviet Math. Dokl. 13 (1972), pp. 1185-1189).
  • [4] R. W. Bagley, E. H. Connell and J. D. McKnight, On properties characterizing pseudocompact spaces, Proc. Amer. Math. Soc. 9 (1958), pp. 500-506.
  • [5] R. Engelking, Outline of General Topology, Warszawa and Amsterdam 1968.
  • [6] S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), pp. 107-115.
  • [7] S. P. Franklin, Spaces in which sequences suffice II, ibid. 61 (1967), pp. 51-56.
  • [8] L. Gillman and M. Jerison, Rings of Continuous Functions, Princeton, N. J., 1960.
  • [9] K. Kunen, Some points in βN, to appear.
  • [10] C. T. Liu, An equivalent condition for the existence of a measurable cardinal, Proc. Amer. Math. Soc. 23 (1969), pp. 605-607.
  • [11] E. Michael, Bi-quotient maps and cartesian products of quotient maps, Ann. Inst. Fourier (Grenoble) 18 (2) (1968), pp. 287-302.
  • [12] E. Michael, A quintuple quotient quest, General Topology and Appl. 2 (1972), pp. 91-138.
  • [13] E. Michael, Countably bi-quotient maps and A-spaces, Topology Conf., Virginia Polytech. Inst. and State Univ., 1973, pp. 183-189. Lecture Notes in Mathematics, Vol. 375, Springer, 1974.
  • [14] K. Morita and S. Hanai, Closed mappings and metric spaces, Proc. Japan Acad. 32 (1956), pp. 10-14.
  • [15] R. C. Olson, Bi-quotient maps, countably bi-sequential spaces, and related topics, General Topology and Appl. 4 (1974), pp. 1-28.
  • [16] F. Siwiec, Sequence-covering and countably bi-quotient mappings, ibid. 1 (1971), pp. 143-154.
  • [17] F. Siwiec, On the theorem of Morita and Hanai, and Stone, Proceedings Second Pittsburgh International Conference on General Topology, 1972, pp. 449-454. Lecture Notes in Mathematics, Vol. 378, Springer, 1974.
  • [18] F. Siwiec, On defining a space by a weak base, Pacific J. Math. 52 (1974), pp. 233-245.
  • [19] F. Siwiec and V. J. Mancuso, Relations among certain mappings and conditions for their equivalence, General Topology and Appl. 1 (1971), pp. 34-41.
  • [20] A. H. Stone, Metrizability and decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), pp. 690-700.
  • [21] G. T. Whyburn, Accessibility spaces, ibid. 24 (1970), pp. 181-185.
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