Density topology and pointwise convergence

Authors

  • Wladyslaw Wilczynski Lodz University

DOI:

https://doi.org/10.4995/agt.2003.2048

Keywords:

Approximately continuous functions, I-approximately continuous functions, topology of pointwise convergence

Abstract

We shall show that the space of all approximately continuous functions with the topology of pointwise convergence is not homeomorphic to its category analogue.

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Author Biography

Wladyslaw Wilczynski, Lodz University

Faculty of Mathematics

References

A.V. Arkhangel'skii, Prostranstwa funktsii v topologii potochechnoi skhodimosti (Spaces of functions in the topology of pointwise convergence), General topology, spaces of functions and dimension, MGU Moskva 1985 (in Russian).

T. Bartoszynski, H. Judah, Set theory. On the structure of the Real Line, A.K. Peters, Wellesley 1995.

K. Ciesielski, L. Larson, K. Ostaszewski, I-density continuous functions, Memoirs of AMS 515(1994).

C. Goffman, C.J. Neugebauer, T. Nishiura, Density topology and approximate continuity, Duke Math. J. 28 ( 1961), 497-505. http://dx.doi.org/10.1215/S0012-7094-61-02847-2

E. Lazarow, The coarsest topology of I-approximately continuous functions, Comm. Math. Univ. Carolinae 27 (1986), 695-704.

J.C. Oxtoby Measure and category, Springer Verlag, New York-Heidelberg-Berlin, (1980). http://dx.doi.org/10.1007/978-1-4684-9339-9

W. Poreda, E. Wagner-Bojakowska, The topology of I-approximately continuous functions, Radovi Mat. 2 (1986), 263-277.

W. Poreda, E. Wagner-Bojakowska, W. Wilczy_nski, A category analogue of the density topology Fund. Math. 125 (1985), 167-173.

F.D. Tall, The density topology Pacific J. Math. 62 (1976), 275-284. http://dx.doi.org/10.2140/pjm.1976.62.275

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Published

2003-10-01

How to Cite

[1]
W. Wilczynski, “Density topology and pointwise convergence”, Appl. Gen. Topol., vol. 4, no. 2, pp. 509–512, Oct. 2003.

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