Glasnik Matematicki, Vol. 33, No.1 (1998), 109-114.

EXTENDING OPEN FAMILIES IN NONMETRIC SPACES AND AN APPLICATION TO OVERLAYS

Tadeusz Dobrowolski, Rolando Jimenez and Witold Marciszewski

Department of Mathematics, Pittsburg State University, Pittsburg KS 66762, USA
e-mail: tdobrowo@mail.pittstate.edu

Instituto de Matematicas, Unidad Morelia, Nicolas Romero 150 Col Centro, Morelia, Mexico
e-mail: rolando@gauss.matem.unam.mx

Faculty of Mathematics and Computer Science, Vrije Universiteit, De Boelelaan 1081 a, 1081 HV Amsterdam, The Netherlands
e-mail: wmarcisz@cs.vu.nl


Abstract.   We show that a family U of open subsets of a subset X of a hereditarily normal paracompact space P which is locally finite in P admits a locally finite open extension V in P which is similar to U. We apply this fact to prove an extension theorem for overlays over hereditarily paracompact spaces.

1991 Mathematics Subject Classification.   54D15, 54D20, 54C56.

Key words and phrases.   Hereditarily normal space, hereditarily paracompact space, similar families, overlay.


Full text (PDF) (free access)
Glasnik Matematicki Home Page