Open [class]

The class splinekit.interval.Open is the concrete class that handles the bounded intervals that are left-open and right-open.

This concrete class honors Interval and Bounded; it handles open intervals between a pair of finite real numbers.

class splinekit.interval.open.Open(bounds: Tuple[float, float])

Bases: Interval, Bounded

The bounded interval \(\{x\in{\mathbb{R}}|x_{0}<x<x_{1}\}=(x_{0},x_{1}).\)

property infimum: float: Left endpoint.

property supremum: float: Right endpoint.

property isleftopen: bool: True

property isrightopen: bool: True

property isopen: bool: True

property ishalfopen: bool: False

property isclosed: bool: False

property isleftbounded: bool: True

property isrightbounded: bool: True

property ishalfbounded: bool: False

property isbounded: bool: True

property isdegenerate: bool: False

property isproper: bool: True

property interior: Self: Open((self.infimum, self.supremum))

property closure: Self: Closed((self.infimum, self.supremum))

property diameter: float: self.supremum - self.infimum

property midpoint: float: 0.5 * (self.supremum + self.infimum)

sortorder() → float: self.midpoint

__contains__(x: float) → bool: self.leftbound < x < self.rightbound

static __new__(cls, bounds: Tuple[float, float]) → Self

Creates the bounded open interval \(\{x\in{\mathbb{R}}|x_{0}<x<x_{1}\}=(x_{0},x_{1})\) that contains all numbers that are larger than \(x_{0}\) and smaller than \(x_{1}.\)

Parameters:: bounds – The tuple (infimum, supremum).
Returns:: An Open interval if bounds contains two finite numbers, with the first number being smaller than the second; otherwise, an interval from {RR, Empty, Above, Below}.
Return type:: Interval