Mathematics · Real Analysis
Let Y be a nonempty bounded, open subset of ℝn and let Y¯ denote its closure. Let {Uj}j ≥ 1 be a collection of open sets in ℝn such that Y¯ ⊆ ∪j ≥ 1 Uj. Which of the following statements is always true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1For every subsequence j1, j2, ... we have Y ⊆ ∪k=1∞ Ujk
- 2There exists a subsequence j1, j2, ... such that Y = ∪k=1∞ Ujk
- 3There exists a positive integer N such that Y ⊆ ∪j=1N Uj
- 4There exist finitely many positive integers j1, ..., jN such that Y ⊆ ∪k=1N Ujk✓
Correct answer
There exist finitely many positive integers j1, ..., jN such that Y ⊆ ∪k=1N Ujk
Download Single Question PDF
Save this question and verified answer as a clean study sheet with live clickable link.
👥
Share with Friends & Study Groups
Challenge your peer aspirants on WhatsApp or Telegram to solve this question!
Online Test Series
Start Free Mock Test →Preparing for Mathematics?
Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.
Chapter Practice
Practice Real Analysis MCQs →Want more practice questions on Real Analysis?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Real Analysis