**Geometrical Isomers**

Geometrical isomers are a type of stereoisomers that have the same molecular formula and connectivity but differ in the spatial arrangement of their atoms. These isomers arise due to the presence of double bonds or rings in a molecule, which restrict the rotation around certain bonds.

**1-Bromo-2-chloro-3-fluorocyclopropane**

1-Bromo-2-chloro-3-fluorocyclopropane is a cyclic molecule with three carbon atoms and three halogen atoms (bromine, chlorine, and fluorine) attached to it. The formula of this compound is C3H4BrClF.

**Determining the Number of Geometrical Isomers**

To determine the number of geometrical isomers, we need to identify the double bonds or rings in the molecule. In this case, there are no double bonds present, but there is a cyclopropane ring, which restricts the rotation around the carbon-carbon bonds.

**Isomer 1: Trans-dibromo**

In the trans-dibromo isomer, the bromine atoms are on opposite sides of the cyclopropane ring, and the chlorine and fluorine atoms are on the same side. This arrangement is referred to as "trans" because the substituents on the ring are on opposite sides.

**Isomer 2: Cis-dibromo**

In the cis-dibromo isomer, the bromine atoms are on the same side of the cyclopropane ring, and the chlorine and fluorine atoms are on the opposite side. This arrangement is referred to as "cis" because the substituents on the ring are on the same side.

**Isomer 3: Trans-chloro**

In the trans-chloro isomer, the chlorine atom is on one side of the cyclopropane ring, and the bromine and fluorine atoms are on the opposite side. This arrangement is referred to as "trans" because the substituents on the ring are on opposite sides.

**Isomer 4: Cis-chloro**

In the cis-chloro isomer, the chlorine atom is on the same side of the cyclopropane ring, and the bromine and fluorine atoms are on the same side. This arrangement is referred to as "cis" because the substituents on the ring are on the same side.

**Conclusion**

In summary, there are four geometrical isomers for 1-bromo-2-chloro-3-fluorocyclopropane: trans-dibromo, cis-dibromo, trans-chloro, and cis-chloro. These isomers arise due to the restricted rotation around the carbon-carbon bonds in the cyclopropane ring, leading to different spatial arrangements of the halogen atoms.