Question

Prove that if $f$ is a continuous map which maps every open set to an open set then $f$ is monotonic.

score 183 · Answer 1 · 2021-02-11 07:34:03

183

Views

Prove that if $f$ is a continuous map which maps every open set to an open set then $f$ is monotonic.

Published on 11 Feb 2021 - 7:34

score 196 · Answer 2 · 2026-03-26 02:58:15

196

Views

$f$ Open, Closed and continuous but not a local homeomorphism

Published on 26 Mar 2026 - 2:58

score 75 · Answer 3 · 2021-03-17 08:08:47

75

Views

A surjective linear mapping $L$ from $X$ to $Y$ is open iff there is a constant $c$ for each $y=Lx$ satisfying $\|x\| \leq c \|y\|$

Published on 17 Mar 2021 - 8:08

score 91 · Answer 4 · 2021-03-18 16:22:08

91

Views

Show that $T(O)$ is not open in $Y$

Published on 18 Mar 2021 - 16:22

score 147 · Answer 5 · 2026-03-26 03:00:21

147

Views

Function that is closed but not open and not continuous

Published on 26 Mar 2026 - 3:00

score 183 · Answer 6 · 2021-03-22 02:04:13

183

Views

Homeomorphism of a Torus

Published on 22 Mar 2021 - 2:04

score 34 · Answer 7 · 2021-03-30 11:01:04

34

Views

Show the function is a open map

Published on 30 Mar 2021 - 11:01

score 64 · Answer 8 · 2021-04-15 12:28:48

64

Views

What is an example of an open set A which we can write it in the form of a Cartesian product of two sets $B\times C$? (B and C not necessarily open)

Published on 15 Apr 2021 - 12:28

score 856 · Answer 9 · 2026-03-26 02:55:05

856

Views

If a continuous surjection $f$ is open/closed, then it is an identification.

Published on 26 Mar 2026 - 2:55

score 146 · Answer 10 · 2021-04-24 18:06:47

146

Views

Continuous $f:$ open $\Omega \mapsto Y, Y$ (Banach) $\Rightarrow$ Inverse function is an open map

Published on 24 Apr 2021 - 18:06

score 110 · Answer 11 · 2021-04-25 04:30:03

110

Views

Prove that function $g(x×y)=x+y^2$ is a open map

Published on 25 Apr 2021 - 4:30

score 104 · Answer 12 · 2021-04-28 07:36:09

104

Views

largest open set such that $F(X) = (\operatorname{tr}(X),\det(X))$ is open

Published on 28 Apr 2021 - 7:36

score 47 · Answer 13 · 2026-03-26 03:00:34

47

Views

closed quotient maps and $T_{k}$ spaces with $k \in \{1,2,3\}$

Published on 26 Mar 2026 - 3:00

score 178 · Answer 14 · 2021-05-19 12:38:11

178

Views

Proving this map to be open and that the quotient space is not Hausdorff

Published on 19 May 2021 - 12:38

score 135 · Answer 15 · 2021-05-30 22:06:05

135

Views

Proving operator image is closed

Published on 30 May 2021 - 22:06

List Question

Prove that if $f$ is a continuous map which maps every open set to an open set then $f$ is monotonic.

$f$ Open, Closed and continuous but not a local homeomorphism

A surjective linear mapping $L$ from $X$ to $Y$ is open iff there is a constant $c$ for each $y=Lx$ satisfying $\|x\| \leq c \|y\|$

Show that $T(O)$ is not open in $Y$

Function that is closed but not open and not continuous

Homeomorphism of a Torus

Show the function is a open map

What is an example of an open set A which we can write it in the form of a Cartesian product of two sets $B\times C$? (B and C not necessarily open)

If a continuous surjection $f$ is open/closed, then it is an identification.

Continuous $f:$ open $\Omega \mapsto Y, Y$ (Banach) $\Rightarrow$ Inverse function is an open map

Prove that function $g(x×y)=x+y^2$ is a open map

largest open set such that $F(X) = (\operatorname{tr}(X),\det(X))$ is open

closed quotient maps and $T_{k}$ spaces with $k \in \{1,2,3\}$

Proving this map to be open and that the quotient space is not Hausdorff

Proving operator image is closed

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