Dieter Leseberg

### Erratum to "Improved nearness research II" [Rostock. Math. Kolloq. 66, 87 - 102 (2011)]

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 68, 81 - 82 (2013)

 MSC: 54A05 Topological spaces and generalizations (closure spaces, etc.) 54B30 Categorical methods [See also 18B30] 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54E17 Nearness spaces

Abstract:   \setcounter{section}{2} \setcounter{theorem}{31} \begin{theorem} states that the category CG-SN is bicoreflective in G-SN. \end{theorem} But this theorem has to be replaced by the following one: \setcounter{theorem}{31} \begin{theorem} The category CG-SN is bireflective in G-SN. \end{theorem} \proof For a supergrill space $(X,\mathcal{B}^X,N)$ we set for each $B \in \mathcal{B}^X$: \begin{equation*} N_C(B) := \{ \rho \subset \underline{P} X: \{cl_n(F): F \in \rho\} \subset \bigcup N(B)\}. \end{equation*} Then $(X, \mathcal{B}^X, N_C)$ is a conic supergrill space and $1_X: (X,\mathcal{B}^X,N) \to (X, \mathcal{B}^X, N_C)$ to be the bireflection in demand.

Keywords:   LEADER proximity, supertopological space, LODATO space, supernear space, superclan space, Bounded Topology.

karin.martin@uni-rostock.de
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