We use the terminology from [1, 3, 5]. Denote by Com(X) the set of all non-empty compact subsets of a space X. A set-valued mapping  : X ?! Y associate with each element x of a space X a non-empty subset (x) of a space Y . Let  : X ?! Y be a set-valued mapping. The mapping  is upper (lower) semicontinuous if the set ?1(H) is closed (open) in X for any closed (open) subset H of Y . The mapping  is closed (open) if the set (W) is closed (open) in Y for any closed (open) subset W of X. Let fEn : n 2 N = f0; 1; 2; 3; : : :gg be a sequence of pairwise disjoint topological spaces. The discrete sum E = fEn : n 2 Ng is the continuous signature of universal E-polyalgebras. A structure of an E-hyperalgebra on a non-empty space G is a family fenG : n 2 Ng, where e0G : En  Gn ! G is a single-valued mapping and enG : En  Gn ! G is a set-valued mapping for any n 2 N, n  1. A topological universal hyperalgebra of the signature E or a topological Ehyperalgebra is a family fG; enG : n 2 Ng, where G is a non-empty space, e0G : En  Gn ! G is a single-valued continuous mapping and enG : En  Gn ! G is an uper semicontinuous compactvalued mapping for any n 2 N, n  1. Follows [4, 6, 8, 2, 7] we introduce the following notions. A hipergroup is a hyperalgebra G with a unique binary operation f
g, unary operation f?1g and a quasi-identity e for which: (HG1) x
(y
z) = (x
y)
z for all x; y; z 2 G; (HG2) x 2 e
x \ x
e for any x 2 G; (HG3) x 2 y
z implies y 2 x
z?1 and zy?1
x for all x; y; z 2 G. A hypergroup G is called a polygroup if: (PG1) e is an identity, i.e. x
e = e
x = x for each x 2 G; (PG2) x
x?1 = x?1
x = feg for each x 2 G. If G is a topological space and a hypergroup and the operations f
;?1 g are compact-valued and upper semicontinuous, then G is a topological hypergroup. If G is a topological space and a polyrgroup and the operations f
;?1 g are compact-valued and upper semicontinuous, then G is a topological polygroup. Any topological group is a topological polyrgroup. A Mal'cev polyalgebra is a hyperalgebra G with one ternary set-valued operation m : G3 ?! G such that m(y; x; x) = fyg and y 2 m(x; x; y) for all x; y 2 G. If G is a topological space and m is a compact-valued upper semicontinuous mapping,then G is called a topological Mal'cev polyalgebra. Theorem 1. Let (G;m) be a topological Mal'cev polyalgebra. If G is a T0-space, then G is a T2-space. Theorem 2. Let (G;m) be a topological Mal'cev polyalgebra. Then any congruence on G is open. In particular, Ta( ) = Tq( ) and the projection p : G ?! G= of G onto (G= ; Tq( )) is an open homomorphism. Remark 1. The assertions of Theorems 1 and 2 are not true for topological hypergroups. Remark 2. The assertions of Theorems 1 and 2 are true for topological polygroups and topological homogeneous polyalgebra.