Glasnik matematički, Vol. 37 No. 1, 2002.
Izvorni znanstveni članak
Topologies generated by discrete subspaces
A. Dow
M. G. Tkachenko
V. V. Tkachuk
R. G. Wilson
Sažetak
A topological space X is called discretely generated if for every subset A X we have
A = {D : D A and D is a discrete subspace of X}.
We say that X is weakly discretely generated if A X and A A implies D \ A for some discrete D A. 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.
Ključne riječi
Discretely generated space; weakly discretly generated space; dyadic space; countably tight space
Hrčak ID:
4823
URI
Datum izdavanja:
1.6.2002.
Posjeta: 2.314 *