Definition
145
[07D] Given \(x,zβ X\) the following standard intervals are defined
\[ \begin{aligned} (x,z)& =& \{ yβ X: x{\lt}y{\lt}z \} \\ {} (x,z]& =& \{ yβ X: x{\lt}yβ€ z \} \\ {} (x,β)& =& \{ yβ X: x{\lt}y \} \\ {} [x,z)& =& \{ yβ X: xβ€ y{\lt}z \} \\ {} [x,z]& =& \{ yβ X: xβ€ yβ€ z \} \\ {} [x,β)& =& \{ yβ X: xβ€ y \} \\ {} (-β,z)& =& \{ yβ X: y{\lt} z \} \\ {} (-β,z]& =& \{ yβ X: yβ€ z \} \\ {} (-β,β)& =& X~ ~ . \end{aligned} \]