Strongly irresolvable spaces. (English) Zbl 1122.54002
From the authors’ abstract: A topological space is strongly irresolvable if no nonempty open subspace is resolvable [J. Foran and P. Liebnitz, Rend. Circ. Mat. Palermo, II. Ser. 40, No. 1, 36–141 (1991; Zbl 0725.54024)].
The authors give several characterizations of strong irresolvability, demonstrate the relationships between strong irresolvability, submaximality and hereditary irresolvability and show that strong irresolvability is a not finitely productive faint topological property, while neither submaximality nor hereditary irresolvability is semitopological.
The authors give several characterizations of strong irresolvability, demonstrate the relationships between strong irresolvability, submaximality and hereditary irresolvability and show that strong irresolvability is a not finitely productive faint topological property, while neither submaximality nor hereditary irresolvability is semitopological.
Reviewer: Bernhard Behrens (Göteborg)
MSC:
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 54A10 | Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) |
| 54C10 | Special maps on topological spaces (open, closed, perfect, etc.) |
| 54G20 | Counterexamples in general topology |
| 54G05 | Extremally disconnected spaces, \(F\)-spaces, etc. |
Keywords:
hereditarily irresolvable space; resolvable at a point; submaximal; crowed; homogeneous; extremally disconnected; almost open set; preopen set; locally dense set; semiopen; faintly openCitations:
Zbl 0725.54024References:
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