Boundary and closure relationship

In summary, the conversation discusses the topic of showing the equality between the boundary of a set S and the intersection of the closure and the closure of the complement of S. The speaker also requests for the definitions of "closure" and "boundary" to determine which definitions are being used in this context. The definitions are then provided and the speaker expresses their difficulty in using the definitions to solve the problem. The speaker asks for any help in solving the problem.
  • #1
gamitor
9
0
Dear all,

How can I show that:

The boundary of a set S is equal to the intersection of the closure and the closure of the complement of S ?

boundary.gif


Thanks a lot in advance
 
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  • #2
Can you give us the definition of "closure" and "boundary"?

(That's not just because I want to force you to use the Homework questions template, but in different domains of mathematics there are different definitions of those concepts, so it's important to know which ones you are using).
 
  • #3
CompuChip said:
Can you give us the definition of "closure" and "boundary"?

(That's not just because I want to force you to use the Homework questions template, but in different domains of mathematics there are different definitions of those concepts, so it's important to know which ones you are using).

The definitions are in the following images. I tried to do it by the definitions or by the Boundary=Closure\Interior but I couldn't.

closure.gif

Boundary.gif


Any help would be highly appreciated
 

1. What is the difference between boundary and closure in a relationship?

Boundary refers to the limits and boundaries set in a relationship, such as personal space, emotional boundaries, and communication boundaries. Closure, on the other hand, refers to the process of accepting and moving on from the end of a relationship.

2. How can boundaries and closure impact a relationship?

Healthy boundaries can help maintain a balanced and respectful relationship, while a lack of boundaries can lead to unhealthy dynamics and resentment. Closure can allow individuals to move on and heal from a relationship, but a lack of closure can lead to unresolved feelings and issues.

3. How can individuals establish healthy boundaries in a relationship?

Effective communication is key in setting and maintaining boundaries in a relationship. It is important for both individuals to openly and respectfully communicate their needs and boundaries, and to listen and respect each other's boundaries.

4. Are boundaries and closure always necessary in a relationship?

Boundaries and closure are important aspects of a healthy and respectful relationship, but the specific boundaries and the need for closure may vary from relationship to relationship. Some relationships may require more boundaries and closure than others.

5. Can boundaries and closure change over time in a relationship?

Yes, boundaries and closure can evolve and change over time in a relationship. As individuals grow and change, their needs and boundaries may also change. It is important for individuals to regularly communicate and reassess their boundaries and closure in a relationship.

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