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General literature does not seem to offer a characterisation of topological groups among all topological spaces. Of course, being completely regular (uniform) is necessary, but separation properties, or indeed any sort of "niceness" like pseudo-metrisability are not sufficient, since topological groups cannot have fixed point property.

General literature does not seem to offer a characterisation of topological groups among all topological spaces. Of course, being completely regular (uniform) is necessary, but separation properties, or indeed any sort of "niceness" like pseudo-metrisability are not sufficient, since topological groups, for instance, cannot have fixed point property.

General literature does not seem to offer a characterisation of topological groups among all topological spaces. Of course, being completely regular (uniform) is necessary, but separation properties, or indeed any sort of "niceness" like metrisability are not all, since topological groups cannot have fixed point property.

General literature does not seem to offer a characterisation of topological groups among all topological spaces. Of course, being completely regular (uniform) is necessary, but separation properties, or indeed any sort of "niceness" like pseudo-metrisability are not sufficient, since topological groups cannot have fixed point property.

General literature does nut seem to offer a characterisation of topological groups among all topological spaces. Of course, being completely regular (uniform) is necessary, but separation properties, or indeed any sort of "niceness" like metrisability are not all, since topological groups cannot have fixed point property.

General literature does not seem to offer a characterisation of topological groups among all topological spaces. Of course, being completely regular (uniform) is necessary, but separation properties, or indeed any sort of "niceness" like metrisability are not all, since topological groups cannot have fixed point property.