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In this program

Compactness
Sequential compactness in metric spaces
Heine–Borel
Bolzano–Weierstrass in R^n
Connected
Path-connected spaces
Compactness of continuous images
Extreme value theorem (topological proof)
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Compactness and connectedness

Compactness of continuous images

Introductory topology · Theoretical / proof-based

Topic

Compactness of continuous images

Practice by unit: Compactness and connectedness

Undergraduate Introductory Topology — scope drawn from open topology notes (metric/topological spaces) and typical US intro topology syllabi.

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