Question

Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$

score 237 · Answer 1 · 2026-04-17 05:35:25

237

Views

Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$

Published on 17 Apr 2026 - 5:35

score 81 · Answer 2 · 2026-04-13 05:40:21

81

Views

Definition request: explicit definition of covering compactness in terms of set notation

Published on 13 Apr 2026 - 5:40

score 438 · Answer 3 · 2026-04-10 02:22:28

438

Views

Is the fact true that compact set is in perfect set?

Published on 10 Apr 2026 - 2:22

score 88 · Answer 4 · 2026-04-12 11:22:28

88

Views

Counterexample of intersection characterization of compactness

Published on 12 Apr 2026 - 11:22

score 259 · Answer 5 · 2026-04-13 21:15:49

259

Views

A sequentially compact metric space is bounded. Help me fix this proof.

Published on 13 Apr 2026 - 21:15

score 641 · Answer 6 · 2026-04-14 03:15:09

641

Views

Second countable spaces under continuous closed surjective maps

Published on 14 Apr 2026 - 3:15

score 874 · Answer 7 · 2026-04-12 01:21:38

874

Views

Motivation of paracompactness

Published on 12 Apr 2026 - 1:21

score 220 · Answer 8 · 2026-04-12 19:43:59

220

Views

Show that every nearly compact space is almost compact space but the converse is not true

Published on 12 Apr 2026 - 19:43

score 686 · Answer 9 · 2026-04-12 12:58:45

686

Views

Compact subsets of metric space with French railway metric

Published on 12 Apr 2026 - 12:58

score 88 · Answer 10 · 2026-04-15 13:47:34

88

Views

Is the set of functions of the form $\int_a^x f(t) dt$, where $f(t)\in A$, which is a bounded subset of $C_{[a,b]}$, closed?

Published on 15 Apr 2026 - 13:47

score 98 · Answer 11 · 2026-04-09 18:38:42

98

Views

Failing to recognize the importance of compactness, connectedness, and other topological notions in Real Analysis

Published on 09 Apr 2026 - 18:38

score 90 · Answer 12 · 2026-04-14 23:38:49

90

Views

Let $A\subset \Bbb R^2 $ with the property that every continuous function on $A$ has a maximum in $A$ .Prove that $A$ is compact.

Published on 14 Apr 2026 - 23:38

score 99 · Answer 13 · 2026-04-16 02:33:41

99

Views

Suppose $X$ is normal space and $\mu$ is a Radon measure, then the union of open null sets is again a null set.

Published on 16 Apr 2026 - 2:33

score 1.1k · Answer 14 · 2026-04-09 05:16:09

1.1k

Views

Cartesian Product of Compact Set and Non-Compact Set is Non-Compact

Published on 09 Apr 2026 - 5:16

score 64 · Answer 15 · 2026-04-16 19:00:05

64

Views

show a set is open

Published on 16 Apr 2026 - 19:00

List Question

Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$

Definition request: explicit definition of covering compactness in terms of set notation

Is the fact true that compact set is in perfect set?

Counterexample of intersection characterization of compactness

A sequentially compact metric space is bounded. Help me fix this proof.

Second countable spaces under continuous closed surjective maps

Motivation of paracompactness

Show that every nearly compact space is almost compact space but the converse is not true

Compact subsets of metric space with French railway metric

Is the set of functions of the form $\int_a^x f(t) dt$, where $f(t)\in A$, which is a bounded subset of $C_{[a,b]}$, closed?

Failing to recognize the importance of compactness, connectedness, and other topological notions in Real Analysis

Let $A\subset \Bbb R^2 $ with the property that every continuous function on $A$ has a maximum in $A$ .Prove that $A$ is compact.

Suppose $X$ is normal space and $\mu$ is a Radon measure, then the union of open null sets is again a null set.

Cartesian Product of Compact Set and Non-Compact Set is Non-Compact

show a set is open

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