Could you explain how to show 7.9 in detail? **Definition.** Let $ X $ and $ Y $ be topological spaces. A function or map $ f : X \rightarrow Y $ is a *continuous function* or *continuous map* if and only if for every open set $ U $ in $ Y $, $ f^{-1}(U) $ is open in $ X $.**Definition.** Let $ f : X \rightarrow Y $ be a function between topological spaces $ X $ and $ Y $, and let $ x \in X $. Then $ f $ is *continuous at the point* $ x $ if and only if for every open set $ V $ containing $ f(x) $, there is an open set $ U $ containing $ x $ such that $ f(U) \subseteq V $. Thus a function $ f : X \rightarrow Y $ is continuous if and only if it is continuous at each point.**Theorem 7.9.** If $ f : X \rightarrow Y $ and $ g : Y \rightarrow Z $ are continuous, then their composition $ g \circ f : X \rightarrow Z $ is continuous.

Name: Could you explain how to show 7.9 in detail? **Definition.** Let $ X
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Description: Could you explain how to show 7.9 in detail? **Definition.** Let \( X $ and $ Y $ be topological spaces. A function or map $ f : X \rightarrow Y $ is a *continuous function* or *continuous map* if and only if for every open set $ U $ in \( Y \

The given theorem is as follows. If f:X→Y,g:Y→Z are continuous, then their composition g∘f:X→Z is…

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Z are continuous, then their composition Theorem 7.9. If f : X → Y and g gof : X → Z is continuous. : Y

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Could you explain how to show 7.9 in detail?

**Definition.** Let $ X $ and $ Y $ be topological spaces. A function or map $ f : X \rightarrow Y $ is a *continuous function* or *continuous map* if and only if for every open set $ U $ in $ Y $, $ f^{-1}(U) $ is open in $ X $.

**Definition.** Let $ f : X \rightarrow Y $ be a function between topological spaces $ X $ and $ Y $, and let $ x \in X $. Then $ f $ is *continuous at the point* $ x $ if and only if for every open set $ V $ containing $ f(x) $, there is an open set $ U $ containing $ x $ such that $ f(U) \subseteq V $. Thus a function $ f : X \rightarrow Y $ is continuous if and only if it is continuous at each point.

**Theorem 7.9.** If $ f : X \rightarrow Y $ and $ g : Y \rightarrow Z $ are continuous, then their composition $ g \circ f : X \rightarrow Z $ is continuous.

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