In this paper, we establish an interesting relation between left thickness and topological left thickness in semigroups by showing that a Borel subset
T
T
of a locally compact semigroup
S
S
is topological left thick in
S
S
iff a certain subset
M
T
{M_T}
associated with
T
T
is left thick in a semigroup
S
1
{S_1}
containing
S
S
, or equivalent, iff
M
T
{M_T}
contains a left ideal of
S
1
{S_1}
. Our results contain a topological analogue of a result of H. Junghenn in [Amenability of function spaces on thick subsemigroups, Proc. Amer. Math. Soc. 75 (1979), 37-41]. However, even in the case of discrete semigroups, our results are more general and in a way more natural than those of Junghenn’s. Furthermore, the fact that
M
T
{M_T}
is left thick iff it contains a left ideal in
S
1
{S_1}
is quite surprising, since in general, a left thick subset need not contain a left ideal although the converse is always true.