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Is the image of an open set under a continuous mapping need not be open?
Wiki User
∙ 12y ago
f(x) = x^{2} is a continuous function on the set R of real numbers, and (-1, 1) is an open set in R, but f(-1, 1) = [0, 1), and [0, 1) is not an open set in R. So, f is not an open function on R.
Wiki User
∙ 12y ago
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What is an image in math?
It is the output of a function.A function is a mapping that associates an image to each pre-image. The term is often used in the context of transformations but need not be restricted to that use.It is the output of a function.A function is a mapping that associates an image to each pre-image. The term is often used in the context of transformations but need not be restricted to that use.It is the output of a function.A function is a mapping that associates an image to each pre-image. The term is often used in the context of transformations but need not be restricted to that use.It is the output of a function.A function is a mapping that associates an image to each pre-image. The term is often used in the context of transformations but need not be restricted to that use.
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It is the output of a function.A function is a mapping that associates an image to each pre-image. The term is often used in the context of transformations but need not be restricted to that use.It is the output of a function.A function is a mapping that associates an image to each pre-image. The term is often used in the context of transformations but need not be restricted to that use.It is the output of a function.A function is a mapping that associates an image to each pre-image. The term is often used in the context of transformations but need not be restricted to that use.It is the output of a function.A function is a mapping that associates an image to each pre-image. The term is often used in the context of transformations but need not be restricted to that use.
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It is simply a mapping. It could be a function but there are several conditions that need to be met before the mapping can become a function and there is no basis for assuming that those conditions are met.
What is the mapping between a set of inputs and a set out outputs?
It is simply a mapping. It could be a function but there are several conditions that need to be met before the mapping can become a function and there is no basis for assuming that those conditions are met.
How do you know mapping is function or not?
A mapping is a rule that defines an association between two sets: a domain and a codomain (which need not be different from the domain).For a mapping to be a function, each element in the domain must have a unique image in the codomain.Sometimes, it is necessary to define the domain so that this requirement is satisfied. For example, square root is not a function from the set of Reals (R) to the Reals (R)because there is no image for a negative number. Also, any positive element of R can be mapped to the principal square root or its negative value. You can get around this by defining the domain as the non-negative real numbers, R0+, and the codomain as either the same or the non-positive real numbers.A mapping is a rule that defines an association between two sets: a domain and a codomain (which need not be different from the domain).For a mapping to be a function, each element in the domain must have a unique image in the codomain.Sometimes, it is necessary to define the domain so that this requirement is satisfied. For example, square root is not a function from the set of Reals (R) to the Reals (R)because there is no image for a negative number. Also, any positive element of R can be mapped to the principal square root or its negative value. You can get around this by defining the domain as the non-negative real numbers, R0+, and the codomain as either the same or the non-positive real numbers.A mapping is a rule that defines an association between two sets: a domain and a codomain (which need not be different from the domain).For a mapping to be a function, each element in the domain must have a unique image in the codomain.Sometimes, it is necessary to define the domain so that this requirement is satisfied. For example, square root is not a function from the set of Reals (R) to the Reals (R)because there is no image for a negative number. Also, any positive element of R can be mapped to the principal square root or its negative value. You can get around this by defining the domain as the non-negative real numbers, R0+, and the codomain as either the same or the non-positive real numbers.A mapping is a rule that defines an association between two sets: a domain and a codomain (which need not be different from the domain).For a mapping to be a function, each element in the domain must have a unique image in the codomain.Sometimes, it is necessary to define the domain so that this requirement is satisfied. For example, square root is not a function from the set of Reals (R) to the Reals (R)because there is no image for a negative number. Also, any positive element of R can be mapped to the principal square root or its negative value. You can get around this by defining the domain as the non-negative real numbers, R0+, and the codomain as either the same or the non-positive real numbers.
