HUNTERTUTORING

Answer Key — Compactness and connectedness

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Introductory topology

Do not share with students before practice tests.

Worksheets — Sets 1–10

| Set | Guidance | | --- | --- | | Set 1 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 2 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 3 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 4 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 5 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 6 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 7 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 8 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 9 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 10 | Compactness and connectedness — verify written work and accept reasonable drawings. |

Worksheets — Sets 11–20

| Set | Guidance | | --- | --- | | Set 11 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 12 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 13 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 14 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 15 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 16 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 17 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 18 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 19 | Compactness and connectedness — verify written work and accept reasonable drawings. | | Set 20 | Compactness and connectedness — verify written work and accept reasonable drawings. |

Review tiers 1–10

  • Checklists are parent-judged.
  • Written items: verify against practice set patterns.
  • Standard text: Compactness: open covers and sequential compactness in metric spaces Heine–Borel and Bolzano–Weierstrass in R^n Connected and path-connected spaces; components Compactness of continuous images and extreme value theorem (topological proof) Introduction to homotopy and the fundamental group (preview)

Practice test scoring

| Tier | Pass guidance | | --- | --- | | 1–3 | Most oral tasks smooth; majority of written correct | | 4–6 | 7/10+ total with clear understanding | | 7–8 | 9/12+ with explanations | | 9–10 | Near-perfect; ready to move on |

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