Questions tagged [sorgenfrey-line]

For questions about the Sorgenfrey line ($\mathbb{R}$ with the lower limit topology) and closely related spaces.

The Sorgenfrey line is obtained by giving $\mathbb{R}$ the lower limit topology, i.e., the topology generated by the family of all half-open intervals of the form $[a,b)$ for $a < b$.

It is a standard counterexample in general topology, and was the first example of a paracompact space whose square (called the Sorgenfrey plane) is not paracompact.

This tag is meant for questions particularly about the Sorgenfrey line, and closely related space, such as it's square.

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Sorgenfrey-Line, [x, ->) represented as a union of half-intervals

Given that $x \in R:$ $$[x,\rightarrow ) := \{y \in R\ | \ y \ge x \} = \bigcup \{[x, x + n) \ | \ n \in N\} $$ What I don't understand here is why the right equality holds (from which will follow that $[x,\rightarrow )$ is open)? Could you please…
Aelx
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