What’s on the Compactness poster
A 6-row table: Statement · Status.
Compactness is finiteness for infinite sets.
- Every open cover has a finite subcover — The definition itself
- Closed and bounded — Equivalent in ℝⁿ only
- Sequentially compact — Equivalent in metric spaces
- Continuous image of a compact set — Compact, always
- Continuous f on a compact set — Attains its max and min
- Compact set in a metric space — Always closed and bounded
Closed and bounded means compact in ℝⁿ and nowhere else. The closed unit ball of an infinite-dimensional space is not compact.
Questions about the Compactness poster
- What’s on the Compactness poster?
- A 6-row table: Statement · Status. Compactness is finiteness for infinite sets. Every open cover has a finite subcover — The definition itself; Closed and bounded — Equivalent in ℝⁿ only; Sequentially compact — Equivalent in metric spaces; Continuous image of a compact set — Compact, always; Continuous f on a compact set — Attains its max and min; Compact set in a metric space — Always closed and bounded. Closed and bounded means compact in ℝⁿ and nowhere else. The closed unit ball of an infinite-dimensional space is not compact.
- Who is the Compactness poster for?
- Compactness belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning analysis can pin it up — a beginner, a student mid-course, or someone revising years later.
- When should you use the Compactness poster?
- Compactness is what turns an infinite argument into a finite one. A wall chart earns its place by being glanceable from where the work is happening, so Compactness belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Compactness?
- Bolzano-Weierstrass, Absolute vs Conditional and Cauchy Sequences sit alongside Compactness in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Bolzano-WeierstrassAbsolute vs ConditionalCauchy Sequences
- Is the Compactness poster free to download and print?
- Yes. Compactness downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
- What size does the Compactness poster print at?
- Compactness is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Compactness loses nothing.Printing guide
Related posters
Charts that sit alongside Compactness on the same wall.
Browse every Mathematics poster, or start from the full catalogue.