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Duality Theorems and Properties of Function Spaces

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Abstract

Section 1.1 introduces some advanced concepts of set theory. We give the statements and applications of the continuum hypothesis, Martin’s axiom and Jensen’s axiom. The next thing under the study is the behavior of spread, hereditary Lindelöf number and hereditary density in function spaces.

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Notes

  1. 1.

    The bibliography of this book is intended to reflect the state of the art of modern C p -theory; besides, it is obligatory to mention the work of all authors whose results, in one form or another, are cited here. The bibliographic selection for this volume has 300 items to solve the proportional part of the task.

References

The bibliography of this book is intended to reflect the state of the art of modern C p -theory; besides, it is obligatory to mention the work of all authors whose results, in one form or another, are cited here. The bibliographic selection for this volume has 300 items to solve the proportional part of the task.

  • [1978] The structure and classification of topological spaces and cardinal invariants (in Russian), Uspehi Mat. Nauk, 33:6(1978), 29–84.

    Google Scholar 

  • [1989b] Hereditarily Lindelof spaces of continuous functions, Moscow University Math. Bull., 44:3(1989), 67–69.

    Google Scholar 

  • [1992a] Topological Function Spaces (translated from Russian), Kluwer Academic Publishers, Dordrecht, 1992.

    Google Scholar 

  • [1996b] On spread and condensations, Proc. Amer. Math. Soc., 124:11(1996b), 3519–3527.

    Google Scholar 

  • Arhangel’skii, A.V., Ponomarev, V.I. [1974] Basics of General Topology in Problems and Exercises (in Russian), Nauka, Moscow, 1974.

    Google Scholar 

  • Baturov D.P. [1987] On subspaces of function spaces (in Russian), Vestnik Moskovsk. Univ., Math., Mech., 42:4(1987), 66–69.

    Google Scholar 

  • [1975] Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa, 1975.

    Google Scholar 

  • Christensen, J.P.R. [1974] Topology and Borel Structure, North Holland P.C., Amsterdam, 1974.

    MATH  Google Scholar 

  • Fremlin, D.H. [1977] K-analytic spaces with metrizable compacta, Mathematika, 24(1977), 257–261.

    Article  MathSciNet  Google Scholar 

  • Gerlits, J. [1983] Some properties of C(X), II, Topology Appl., 15:3(1983), 255–262.

    Google Scholar 

  • [1977] Topological spaces without κ-accessible diagonal, Comment. Math. Univ. Carolinae, 18:4(1977), 777–788.

    Google Scholar 

  • [1980] Cardinal Functions in Topology—Ten Years Later, Mathematical Centre Tracts, North Holland P.C., Amsterdam, 1980.

    Google Scholar 

  • [1991] Cardinal functions, Recent Progress in General Topology, North-Holland, Amsterdam, 1992, 417–441.

    Google Scholar 

  • Kunen, K. [1980] Set Theory. An Introduction to Independence Proofs, Studies Logic Found. Mathematics, 102(1980), North Holland P.C., Amsterdam, 1980

    Google Scholar 

  • Kuratowski, C. [1966] Topology, vol. 1, Academic Press Inc., London, 1966.

    Google Scholar 

  • Lutzer, D.J., Mill, J. van, Pol, R. [1985] Descriptive complexity of function spaces, Transactions of the Amer. Math. Soc., 291(1985), 121–128.

    Article  MATH  Google Scholar 

  • Pytkeev, E.G. [1976] Upper bounds of topologies, Math. Notes, 20:4(1976), 831–837.

    Google Scholar 

  • [1992a] On Fréchet–Urysohn property of spaces of continuous functions, (in Russian), Trudy Math. Inst. RAN, 193(1992a), 156–161.

    Google Scholar 

  • [1991] Methods of the theory of cardinal invariants and the theory of mappings applied to the spaces of functions (in Russian), Sibirsk. Mat. Zhurnal, 32:1(1991), 116–130.

    Google Scholar 

  • [1994] Decomposition of C p (X) into a countable union of subspaces with “good” properties implies “good” properties of C p (X), Trans. Moscow Math. Soc., 55(1994), 239–248.

    Google Scholar 

  • [1995] What if C p (X) is perfectly normal? Topology Appl., 65(1995), 57–67.

    Google Scholar 

  • Todorcevic, S. [1989] Partition Problems in Topology, Contemporary Mathematics, American Mathematical Society, 84(1989). Providence, Rhode Island, 1989.

    Google Scholar 

  • Velichko, N.V. [1981] On weak topology of spaces of continuous functions (in Russian), Matematich. Zametki, 30:5(1981), 703–712.

    Google Scholar 

  • Zenor, Ph. [1980] Hereditary m-separability and hereditary m-Lindelöf property in product spaces and function spaces, Fund. Math., 106(1980), 175–180.

    MATH  MathSciNet  Google Scholar 

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Tkachuk, V.V. (2014). Duality Theorems and Properties of Function Spaces. In: A Cp-Theory Problem Book. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-04747-8_1

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