Step 1: Understanding the Concept
Critical temperature \(T_c\) is the highest temperature at which a gas can be liquefied by applying pressure.
Step 2: Analysing the statements
Above \(T_c\) the kinetic energy of molecules is too high for intermolecular attraction to hold them as a liquid, however large the pressure.
A gas still exists as a gas at lower temperatures, and its volume never becomes zero or double at this point.
Step 3: Compare the options
The statement that matches is that above this temperature the gas cannot be liquefied by increasing pressure.
Final Answer:
Above the critical temperature a gas cannot be liquefied by raising the pressure.
\[ \boxed{\text{(A) }\text{above which gas cannot be liquified by increasing pressure.}} \]