Compactness and Connectedness MCQs

Prepare for Compactness and Connectedness MCQs with verified questions, past-paper solutions, and conceptual explanations for CSS, PMS, FPSC, PPSC, and NTS examinations.

15 Solved Questions • 12 Mins Practice • Updated for 2026 Competitive Exams
MCQS
2026 Solved Edition · Updated October 2026 · Verified Editorial Standards

Welcome to the verified preparation module for Compactness and Connectedness MCQs on McqsMind. This comprehensive set offers solved multiple-choice questions with answers, detailed explanations, and authentic past-paper style questions aligned with the latest syllabus of Topology (Mathematics).

100% Verified Answer Keys CSS, PMS, FPSC, PPSC, NTS Ready 2026/2027 Syllabus Guidelines

Direct Definition & Conceptual Scope

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Compactness and Connectedness constitutes an essential examination topic within Mathematics, evaluating theoretical principles, historical context, and practical problem-solving applications. On MCQsMind, candidates practice verified past-paper solutions, conceptual breakdowns, and syllabus-aligned questions tailored for CSS, PMS, and competitive screening examinations.

Solved Questions

Practice with answers, explanations, and exam-focused revision notes.

15 MCQs Page 1

High-Yield Exam Revision Cheat Sheet & Mnemonics

Essential exam standard definitions and formulas for rapid 2-minute revision

High-Frequency Articles
  • Art. 6: High Treason
  • Art. 9: Security of Person
  • Art. 19-A: Right to Information
  • Art. 25-A: Free Education (5–16 yrs)
Federalism & Provinces
  • Art. 140-A: Local Government
  • Art. 153: Council of Common Interests
  • Art. 160: National Finance Commission
  • Art. 175-A: Judicial Commission (JCP)
Islamic Provisions
  • Art. 2: Islam as State Religion
  • Art. 2A: Objectives Resolution Substantive
  • Art. 203: Federal Shariat Court (FSC)
  • Art. 228: Council of Islamic Ideology

Topic Notes: Compactness and Connectedness

Quick Revision 3 min read 12 key points
Section 1 of 3

1 1. Fundamentals of Connectedness

4 points
  • Definition
    Connected Space: A topological space X is connected if it cannot be represented as the union of two disjoint, non-empty open sets. This implies there is no 'separation' of the space into distinct components.
  • Theory
    Continuous Image: The continuous image of a connected space is always connected. If f: X → Y is continuous and X is connected, then f(X) is connected in Y.
  • Definition
    Path-Connectedness: A space X is path-connected if for any two points x, y in X, there exists a continuous map f: [0, 1] → X such that f(0)=x and f(1)=y. Path-connectedness is a stronger condition than connectedness.
  • Comparison
    Connected vs Path-Connected: Every path-connected space is connected, but the converse is false. The Topologist’s Sine Curve is the classic example of a space that is connected but not path-connected.
Section 1 / 3
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1
What is the property of a space where every open cover has a finite subcover?
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2
Which condition is necessary for a space to be compact in the sense of the finite intersection property?
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3
A space is totally disconnected if its only connected subsets are:
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4
Which of the following is a connected subset of the plane R^2?
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5
The one-point compactification of the real line is homeomorphic to which of the following?
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6
A space is sequentially compact if every sequence has a convergent subsequence. In metric spaces, sequential compactness is equivalent to:
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7
What is the image of a connected space under a continuous function?
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8
In the context of the Heine-Borel theorem, a subset of Euclidean space is compact if and only if it is:
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9
Which of the following is a property of a locally connected space?
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10
What is the product of two compact spaces under the product topology?
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Pedagogical Syllabus Blueprint

Compactness and Connectedness MCQs: Preparation Strategy & Exam Blueprint

Examination Weightage & Commission Distribution

In Pakistan's premier competitive examinations—including the Federal Public Service Commission (FPSC General Recruitment & CSS MPT), Punjab Public Service Commission (PPSC Lecturer, Tehsildar & PMS Screening), KPPSC, SPSC, and BPSC—questions derived from Compactness and Connectedness MCQs consistently constitute a decisive 10% to 25% weightage of the Topology paper. Testing agencies frequently evaluate both foundational factual recall and deeper analytical comprehension, requiring aspirants to master key dates, statutory articles, constitutional clauses, and thematic definitions.

High-Yield Conceptual Pillars & Distractor Analysis

Historical trend analysis across past five-year examination cycles demonstrates that examiner traps frequently involve closely matched numerical alternatives, chronologically contiguous treaties, and semantic subtleties in statutory phraseology. When preparing Compactness and Connectedness MCQs, candidates must deliberately review the underlying rationale provided for every question rather than merely memorizing raw answer options. Understanding why incorrect distractors fail is the most reliable predictor of achieving top percentiles in computerized and optical mark recognition (OMR) screening tests.

Negative Marking Mitigation & Time Management Protocol

For examinations enforcing negative marking penalties (such as PPSC's 0.25-mark deduction per erroneous response or NTS gatekeeper quotas), an aggressive elimination technique must be deployed. Candidates should systematically rule out improbable options first to elevate probability thresholds from 25% to 50% or 100%. Allocating an average of 45 to 60 seconds per item during mock trials builds the psychological stamina and cognitive precision required to complete 100-question papers within official 90-minute time limits.

Recommended Reference Sources & Statutory Reading

To achieve definitive conceptual mastery in Mathematics, candidates are advised to cross-reference our solved explanations with primary gazettes, statutory texts, and canonical academic textbooks. Verifying controversial questions against authentic official repositories guarantees that prospective civil servants and professional candidates present incontestable answers during both optical paper evaluations and viva voce departmental interviews.