Density topology and pointwise convergence

Wladyslaw Wilczynski
DOI: https://doi.org/10.4995/agt.2003.2048

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.


Keywords

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

Full Text:

PDF

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

Abstract Views

1418
Metrics Loading ...

Metrics powered by PLOS ALM


Bookmark and Share


Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt