Recently, bottles made of PET (polyethylene terephthalate) are widely used for containers containing drinks such as juices so on.  In order to keep a PET bottle either cold or a desired temperature, cold insulators for PET bottles are available on the market.  Such insulators are formed in a tubular shape with a bottom similar to that of PET bottles.  The insulator can be held with hand or can be put in a bag and the like when an inlet for the PET bottle on the insulator is closed in a form of a drawstring bag-like-state as a result of pulling the string provided to the inlet. 
The inventor previously developed such a thermal insulator having a string for holding the insulator to the body part of a holder and having a member for detach that is used for dividing the insulator into two parts adjacent to a center part of string.  In this way, the string can be connected when the insulator is used, on the contrary, the string can not be connected when it is unused.  Consequently, the insulator can be carried in a state of suspension from a bag and the like. 
The previously developed insulator, however, has the following problems to solve.  At first, the members for detachment provided to the forefront of the string get in the way when the insulator is divided.  Secondly, it is unsanitary with insulators, because the neck of the bottle and vicinity thereof are exposed from the holder during the use.  The same problem is observed especially when a bottle is exposed outside, not housed in a bag and the like.  In order to solve the second problem, the height of insulator may be increased so as to cover a part of the bottle including its neck.  In such case, no problem occurs from a hygiene point of view, however, a person who drink the content of the bottle needs to take the bottle out whenever they try to drink.  Similar problem is also observed not only a PET bottle, but also any other tubular shaped case into which foods/drinks are contained.