The question seems to be asking for a characteristic of points in continuous functions. Based on standard mathematical theory, continuous functions have points that are connected. This is because, in topological terms, a continuous function maps connected sets to connected sets, meaning the graph of a continuous function does not have any sudden jumps or breaks between points.

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Here are five related questions for expanding your understanding:

1. What is the formal definition of a continuous function?
2. How is the concept of limits related to continuity?
3. What is the difference between continuous and discontinuous functions?
4. How do continuous functions behave on closed intervals?
5. Can a continuous function have any isolated points?

Tip: Continuity in functions ensures that small changes in the input produce small changes in the output, making the function "smooth" without abrupt changes.