| 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.