Is (2, 3) a Closed Set in the Phase Space X = [0, 1] ∪ (2, 3)?

In summary, phase space is a mathematical concept used to describe the possible states of a physical system. It is used to study the behavior and dynamics of physical systems, by plotting the possible states in multi-dimensional space. An open set in phase space includes all possible states except for boundary points, while a closed set includes all possible states including boundary points. Open and closed sets are important in phase space as they help define and limit possible states and play a crucial role in determining a system's behavior and evolution.
  • #1
burak100
33
0
[itex]X = [0, 1] \bigcup (2,3)[/itex] is phase space.

Show that [itex](2, 3) [/itex] open and closed set of [itex] X [/itex] .

the question is like that but I think it is false because it is not close, right?
 
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  • #2
I'm not sure what "phase space" has to do with this. This is a general topology question.

What makes you think it is not closed? What limit point of the set is there that is not in the set?

(Be very, very careful about the points 2 and 3!)
 
  • #3
is it true?
Limit point of (2, 3) ---> again (2, 3) in X. then (2, 3) is closed in X.
 

1. What is phase space?

Phase space is a mathematical concept used in physics and engineering to describe the possible states of a physical system. It is a multi-dimensional space where each dimension represents a different variable or property of the system, and each point in the space represents a specific state of the system.

2. How is phase space used?

Phase space is used to study the behavior and dynamics of physical systems. By plotting the possible states of a system in phase space, scientists can analyze how the system evolves over time and make predictions about its future behavior.

3. What is an open set in phase space?

In phase space, an open set is a region that includes all possible states of a system, except for the boundary points. These boundary points are excluded because they may represent physically impossible states or states that are not of interest to the study.

4. What is a closed set in phase space?

A closed set in phase space is a region that includes all possible states of a system, including the boundary points. This means that every point within the set is a legitimate state of the system and is relevant to the study.

5. Why are open and closed sets important in phase space?

Open and closed sets are important in phase space because they help define and limit the possible states that a system can have. They also play a crucial role in determining the behavior and evolution of a system, as well as in making predictions about its future states.

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