12 questions linked to/from Examples of Baire class 2 functions
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### Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?

Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true? It seems to me like they are equal definitions in a way. Can you give me a counter-example? Thanks
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### Construction of a function which is not the pointwise limit of a sequence of continuous functions

This is somewhat linked to a prior question of mine which was looking to see if a proof of mine regarding the Dirichlet function was correct (it wasn't). I now have an answer to the question which can ...
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### Maximum Baire class of a Riemann integrable function

In this answer (see example 1), AndrĂ©s Caicedo gives an example of a function $f : [0,1] \to \mathbb{R}$ which is Riemann integrable and is (strictly) of second Baire class. Are there Riemann ...
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### Examples of nowhere continuous functions

Do you know examples of nowhere continuous functions, besides the Dirichlet function and its modifications?
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### Examples of functions that do not belong to any Baire class

Recently I read this post, which gives examples of Baire class 2 functions. I have also been reading the Wikipedia article on Baire functions. The article claims that "Henri Lebesgue proved that ... ...
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### What are examples of real-valued functions of Baire class at least 3?

It's quite easy to find functions of Baire classes 0 and 1; however, the regularity of these functions falls off quite quickly, and with it, ease of construction. The most famous example of a Baire ...
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### Is a function with a dense set of points of continuity of Baire Class 1?

Let $f:[0,1]\to\mathbb R$ be an arbitrary function. It is well known that if $f$ is of Baire Class 1, then the points at which $f$ is continuous form a dense subset of $[0,1]$. My question now is, if ...
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### What is an interval contiguous to the Cantor set?

I have been reading the answer to Examples of Baire class 2 functions , and I'm trying to see what is an example of an interval contiguous to the Cantor set. Could someone lend me a hand?