Glasnik Matematicki, Vol. 37, No.1 (2002), 187-210.


A. Dow, M. G. Tkachenko, V. V. Tkachuk and R. G. Wilson

Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3

Departamento de Matematicas, Universidad Autonoma Metropolitana, Av. San Rafael Atlixco 486, Col. Vicentina, Iztapalapa, C. P. 09340 Mexico, D.F.

Abstract.   A topological space X is called discretely generated if for every subset AX we have

A = ∪ {D : DA and D is a discrete subspace of X}.

We say that X is weakly discretely generated if AX and AA implies D \ A ≠ Ø for some discrete DA. It is established that sequential spaces, monotonically normal spaces and compact countably tight spaces are discretely generated. We also prove taht every compact space is weakly discretely generated and under the Continuum Hypothesis any dyadic discretely generated space is metrizable.

2000 Mathematics Subject Classification.   54H11, 54C10, 22A05, 54D25, 54C25.

Key words and phrases.   Discretely generated space, weakly discretly generated space, dyadic space, countably tight space.

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