# Do You Know Compact Space?

10 Questions | Total Attempts: 118  Settings  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).

• 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

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