Continuity and closure

In summary, continuity refers to the uninterrupted progression of a process or system, while closure is the organized conclusion of something. In scientific research, continuity is important for accurate and reliable data and results, and scientists ensure it through controlled variables and standardized procedures. Not having continuity and closure in scientific research could lead to inaccurate data and harmful consequences.
  • #1
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Hi,
can anyone help me ?

Given Topological Spaces (metric spaces) (X, d1) and (Y,d2), show that a function f: X -> Y is continuous if and only if f(cl of A) is a subset of cl of f(A) for all A subset X1.

How can i proof this ?

Thank you!
 
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  • #2
What is your definition of continuous?? What properties did you see already about continuity??

What did you try already to solve this problem??
 

What is continuity?

Continuity refers to the smooth and uninterrupted progression of a process or system without any breaks or interruptions.

What is closure?

Closure is the act of bringing something to an end or conclusion, often in a systematic or organized manner.

Why is continuity important in scientific research?

Continuity is important in scientific research because it ensures that the data and results collected are accurate and reliable. It also allows for the replication of experiments and the building of knowledge over time.

How do scientists ensure continuity in their experiments?

Scientists ensure continuity in their experiments by carefully controlling variables and following standardized procedures. They also document their methods and results to allow for replication by other researchers.

What are the potential consequences of not having continuity and closure in scientific research?

Without continuity and closure, scientific research could result in inaccurate or unreliable data and conclusions. This could lead to wasted time, resources, and even harm to individuals if the research is used to make important decisions or develop treatments.

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