Do there exists nonhomeomorphic closed sets?

yes,

Step-by-step explanation:

Homeomorphic sets :-

Two sets are homeomorphic if define a function f between both sets which is satisfy the following conditions:

 Function f is a bijection (one-to-one and onto),

 Function f is continuous,

 Inverse function of f is also continuous.

example:

Let given by where is a continuous and bijection fuction but inverse of fuction f is discontinuous.

Hence, set   and are not homeomorphic.

answer: okw

step-by-step explanation:

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this