A simple question about uniqueness terminology
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I am reading through a book on topology and came across the following phrase: for each element $xin X$ we can uniquely define a function $f_x: Arightarrow B$ such that $f_x$ satisfies some topological property $P$.
What exactly does this mean? Does this mean that for each $xin X$ there is only one $f_x$ satisfying the property $P$? Or does it mean that if you have different elements $xneq y$ in $X$ then $f_xneq f_y$?
The terminology is a bit confusing to me.
definition
asked Dec 18 '18 at 22:26
foshofosho
4,7711033
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add a comment |
$begingroup$
I am reading through a book on topology and came across the following phrase: for each element $xin X$ we can uniquely define a function $f_x: Arightarrow B$ such that $f_x$ satisfies some topological property $P$.
What exactly does this mean? Does this mean that for each $xin X$ there is only one $f_x$ satisfying the property $P$? Or does it mean that if you have different elements $xneq y$ in $X$ then $f_xneq f_y$?
The terminology is a bit confusing to me.
definition
asked Dec 18 '18 at 22:26
foshofosho
4,7711033
$endgroup$
3
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What book are you referring to? What page? What is the context? How was "topological property" defined in the text? What is $A$, and how does it relate to $X$?
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– Card_Trick
Dec 18 '18 at 22:29
1
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Without the context suggested by @Card_Trick, it is hard to say. However, I would interpret what you have written to mean "For each $x$, we can define a function $f_x$. For any fixed $x$, this function is uniquely defined." That is, once we fix the value of $x$, the function corresponding to that value is unique.
$endgroup$
– Xander Henderson
Dec 18 '18 at 22:32
add a comment |
$begingroup$
I am reading through a book on topology and came across the following phrase: for each element $xin X$ we can uniquely define a function $f_x: Arightarrow B$ such that $f_x$ satisfies some topological property $P$.
What exactly does this mean? Does this mean that for each $xin X$ there is only one $f_x$ satisfying the property $P$? Or does it mean that if you have different elements $xneq y$ in $X$ then $f_xneq f_y$?
The terminology is a bit confusing to me.
definition
asked Dec 18 '18 at 22:26
foshofosho
4,7711033
$endgroup$
I am reading through a book on topology and came across the following phrase: for each element $xin X$ we can uniquely define a function $f_x: Arightarrow B$ such that $f_x$ satisfies some topological property $P$.
What exactly does this mean? Does this mean that for each $xin X$ there is only one $f_x$ satisfying the property $P$? Or does it mean that if you have different elements $xneq y$ in $X$ then $f_xneq f_y$?
The terminology is a bit confusing to me.
definition
definition
asked Dec 18 '18 at 22:26
foshofosho
4,7711033
asked Dec 18 '18 at 22:26
foshofosho
4,7711033
asked Dec 18 '18 at 22:26
foshofosho
4,7711033
asked Dec 18 '18 at 22:26
foshofosho
4,7711033
asked Dec 18 '18 at 22:26
foshofosho
4,7711033
4,7711033
3
$begingroup$
What book are you referring to? What page? What is the context? How was "topological property" defined in the text? What is $A$, and how does it relate to $X$?
$endgroup$
– Card_Trick
Dec 18 '18 at 22:29
1
$begingroup$
Without the context suggested by @Card_Trick, it is hard to say. However, I would interpret what you have written to mean "For each $x$, we can define a function $f_x$. For any fixed $x$, this function is uniquely defined." That is, once we fix the value of $x$, the function corresponding to that value is unique.
$endgroup$
– Xander Henderson
Dec 18 '18 at 22:32
add a comment |
3
$begingroup$
What book are you referring to? What page? What is the context? How was "topological property" defined in the text? What is $A$, and how does it relate to $X$?
$endgroup$
– Card_Trick
Dec 18 '18 at 22:29
1
$begingroup$
Without the context suggested by @Card_Trick, it is hard to say. However, I would interpret what you have written to mean "For each $x$, we can define a function $f_x$. For any fixed $x$, this function is uniquely defined." That is, once we fix the value of $x$, the function corresponding to that value is unique.
$endgroup$
– Xander Henderson
Dec 18 '18 at 22:32
3
3
$begingroup$
What book are you referring to? What page? What is the context? How was "topological property" defined in the text? What is $A$, and how does it relate to $X$?
$endgroup$
– Card_Trick
Dec 18 '18 at 22:29
$begingroup$
What book are you referring to? What page? What is the context? How was "topological property" defined in the text? What is $A$, and how does it relate to $X$?
$endgroup$
– Card_Trick
Dec 18 '18 at 22:29
1
1
$begingroup$
Without the context suggested by @Card_Trick, it is hard to say. However, I would interpret what you have written to mean "For each $x$, we can define a function $f_x$. For any fixed $x$, this function is uniquely defined." That is, once we fix the value of $x$, the function corresponding to that value is unique.
$endgroup$
– Xander Henderson
Dec 18 '18 at 22:32
$begingroup$
Without the context suggested by @Card_Trick, it is hard to say. However, I would interpret what you have written to mean "For each $x$, we can define a function $f_x$. For any fixed $x$, this function is uniquely defined." That is, once we fix the value of $x$, the function corresponding to that value is unique.
$endgroup$
– Xander Henderson
Dec 18 '18 at 22:32
add a comment |
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$begingroup$
What book are you referring to? What page? What is the context? How was "topological property" defined in the text? What is $A$, and how does it relate to $X$?
$endgroup$
– Card_Trick
Dec 18 '18 at 22:29
1
$begingroup$
Without the context suggested by @Card_Trick, it is hard to say. However, I would interpret what you have written to mean "For each $x$, we can define a function $f_x$. For any fixed $x$, this function is uniquely defined." That is, once we fix the value of $x$, the function corresponding to that value is unique.
$endgroup$
– Xander Henderson
Dec 18 '18 at 22:32