The Order Topology
Автор: Aitlantis Civic
Загружено: 2026-02-17
Просмотров: 5
Описание:
A simply ordered set
is a linearly ordered set,
for all a and b,
a is either
smaller than b
or equal to b
or larger than b.
Comparability,
(that’s totality).
Antisymmetry.
Transitivity.
If X is a simply ordered set,
there is the order topology for X.
(If X is a simply ordered set,
there is the order topology for X.)
Let X be a set
with more than one element.
(Let X be a set
with more than one element.)
And X has simple
order relation,
let basis ℬ
be the following collection:
All open intervals
(a,b) in X.
(All open intervals
(a,b) in X).
And if there is a smallest
element in X,
let’s call it lowercase m,
we must include
all right half open
intervals [m,b).
And if there is a largest
element in X,
let’s call it uppercase M,
we must include
all left half open
intervals (a,M].
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Written by Aitlantis Civic
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