Do You Know Compact Space?

10 Questions | By Livyn | Last updated: Mar 20, 2022 | Total Attempts: 122

Questions

Settings

Create your own Quiz

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit point) and bounded (that is, having all its points lie within some fixed distance of each other).

Questions and Answers

1.

Compact Space is studied in ......?
- A.
  
  Mathematics
- B.
  
  History
- C.
  
  Literature
- D.
  
  Music
2.

Compact Space has the following examples except?
- A.
  
  A rectangle
- B.
  
  A closed interval
- C.
  
  A finite set of points
- D.
  
  A triangle
3.

Which sometimes the synonym of compact space?
- A.
  
  Compact set
- B.
  
  Vector space
- C.
  
  Lattices
- D.
  
  Polytopes
4.

In the what century did several disparate mathematical properties were understood that would later be seen as consequences of compactness?
- A.
  
  20th Century
- B.
  
  19th Century
- C.
  
  18th Century
- D.
  
  17th Century
5.

Who had been aware that any bounded sequence of points (in the line or plane, for instance) has a subsequence that must eventually get arbitrarily close to some other point?
- A.
  
  Isaac Newton
- B.
  
  Bernard Bolzano
- C.
  
  Albert Einstein
- D.
  
  James McCaffrey
6.

What year did Bernard Bolzano became aware that any bounded sequence of points (in the line or plane, for instance) has a subsequence that must eventually get arbitrarily close to some other point?
- A.
  
  1928
- B.
  
  1888
- C.
  
  1817
- D.
  
  1785
7.

Bernard Bolzano had been aware that any bounded sequence of points (in the line or plane, for instance) has a subsequence that must eventually get arbitrarily close to some other point, called a .....?
- A.
  
  Decimal point
- B.
  
  Starting point
- C.
  
  Ending point
- D.
  
  Limit point
8.

Bolzano's proof relied on the method of bisection: the sequence was placed into an interval that was then divided into how many parts?
- A.
  
  Two
- B.
  
  One
- C.
  
  Five
- D.
  
  Four
9.

The full significance of Bolzano's theorem, and its method of proof was rediscovered by .....?
- A.
  
  Albert Einstein
- B.
  
  James McCaffrey
- C.
  
  Karl Weierstrass
- D.
  
  Isaac Newton
10.

The full significance of Bolzano's theorem, and its method of proof, would not emerge until almost how many years later when it was rediscovered by Karl Weierstrass?
- A.
  
  50 years
- B.
  
  20 years
- C.
  
  10 years
- D.
  
  100 years