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$\mathbb{R}$ with the lower limit topology is not second-countable

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Is the Sorgenfrey Line second countable?

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The closure of $(0,1)$ in the lower-limit topology on $\mathbb{R}$

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Lower Limit Topology Properties

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Prob. 2, Sec. 28 in Munkres' TOPOLOGY, 2nd ed: Compactness of $[0,1]$ in the lower limit topology

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Why is $\mathfrak{c}$ the cardinality of the lower limit topology on $\mathbb{R}$?

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topology (upper limit and lower limit)

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Cheap proof that the Sorgenfrey line is normal?

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105
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How to prove Sorgenfrey topology stronger than standard?

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Sorgenfrey line is not orderable

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Compact sets of lower limit topology

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Is the given function $f$ continuous?

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Regular topological spaces need not to be normal

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The Sorgenfrey line is a Baire Space

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Every subspace of $\mathbb{R}$ with the lower limit topology is separable

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