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IV Iberoamerican Conference on Topology and its Applications (IV CITA)
April 18-21, 2001
University of Coimbra
Coimbra, Portugal

Organizers
Maria Manuel Clementino, Jorge Picado, Lurdes Sousa, Maria João Ferreira, Gonçalo Gutierres, Dirk Hofmann

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On (\kappa, \mu)-narrow spaces
by
Oleg Okunev
Facultad de Ciencias, UNAM, Mexico
Coauthors: V. Tkachuk (Univ. Autonoma Metropolitana de Mexico, Mexico)

Given two cardinals \kappa and \mu, we say that a Tychonoff space X is (\kappa, \mu)-narrow if for every indexed family U of open sets in X, the set of all points where U has order >= \mu is a neighborhood of the set of all points at which U has order >= \kappa. It turns out that narrowness properties are closely related to the tightness of the space. Furthermore, Cp(X) is (\kappa, \mu)-narrow if and only if for every natural n, every \kappa-sequence of points in Xn has a \mu-accumulation point; in particular, ext*(X) <= \kappa if and only if the space Cp(X) is (\kappa, \omega)-narrow.

Date received: February 28, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafw-41.