Online text: www.jirka.org/ra/
Additional inspected sections: 3.4 Uniform continuity and 7.5 Continuous functions.
Whole-book author: Jiří Lebl; no separately credited chapter author is established. These HTML sections are undated. The author landing page dates the downloadable PDF version 6.3 to 15 May 2026; that version date is not assigned to the HTML.
Cited passages: §3.4.1, Definition 3.4.1 and Theorem 3.4.4; §3.4.2, Lemma 3.4.5; §3.4.3, Proposition 3.4.8 and Example 3.4.10; §7.5.4, Definition 7.5.10 and Theorem 7.5.11.
Author and work verified; edition year and publisher were not verified and are not asserted.
Cited passages: Section 5.1, Example 5.1.4.
Edition year and publisher not verified; no claim made.
Cited passages: Section 5.2, Lemma 5.2.7 and Theorem 5.2.9.
Cited passages: Lebl, Basic Analysis I, §2.1: sequences as functions and their limits.
Cited passages: Lebl, Basic Analysis I, §1.2: approximation of a supremum; Lebl, Basic Analysis I, §1.2: supremum, infimum and attainment.
Additional inspected locators: §1.2.3, Proposition 1.2.6(i) and proof; Proposition 1.2.8; §1.2.5, Exercise 1.2.9. The HTML section is undated; no PDF version date is assigned to it.
Cited passages: Basic Analysis, Volume I by Jiří Lebl, opening footnote to §2.3: the theorem's two namesakes; Basic Analysis, Volume I by Jiří Lebl, §2.3.3, Theorem 2.3.8: every bounded real sequence has a convergent subsequence; Lebl, Basic Analysis I, §2.3: equality of finite bounds and extended limits; Lebl, Basic Analysis I, §2.3: extreme subsequential limits.
Cited passages: Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.1.1, Definition 6.1.1 and Proposition 6.1.5; Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.1.1, Example 6.1.2, even powers on the interval from minus one to one; Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.1.2, Definition 6.1.6 and Proposition 6.1.7.
Cited passages: Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.2.1, Theorem 6.2.2; Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.2.2, Theorem 6.2.4; Basic Analysis: Introduction to Real Analysis, Volume I by Jiří Lebl, §6.2.3, Theorem 6.2.10 and the unbounded-interval observation following its proof.

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