showing 2 related works from this author
Erratum to “Irregularity” [Topology Appl. 154 (8) (2007) 1565–1580]
2012
[2, Proposition 4.4] states that each regular pretopology is topologically regular. Professor F. Mynard (Georgia Southern University) advised the authors that he was not convinced by the proof of that proposition, which enabled us to realize the proposition is wrong, as the example below shows. Recall that (e.g., [2]) a pretopology ξ on a set X is called regular if Vξ (x)⊂ adh ξ Vξ (x) (respectively, topologically regular if Vξ (x)⊂ cl ξ Vξ (x)) for every x ∈ X . As a consequence, in the sequel of [2], regular should be read topologically regular in a few instances, in particular in [2, Theorem 4.6]. [2, Proposition 4.4] is also quoted in [3], where it is used in some reformulations of clas…
Irregularity
2007
AbstractRegular and irregular pretopologies are studied. In particular, for every ordinal there exists a topology such that the series of its partial (pretopological) regularizations has length of that ordinal. Regularity and topologicity of special pretopologies on some trees can be characterized in terms of sets of intervals of natural numbers, which reduces studied problems to combinatorics.