In a neutrosophic Hausdorff topological space
X, the following conditions are equivalent.
Indeed, Hewitt has constructed a regular Hausdorff topological space
S such that the only continuous real-valued functions on it are constant functions; in , Granirer defined a semi-topological semigroup structure on S by letting a.
If S is also a Hausdorff topological space
and the binary operation is continuous for the product topology of S x S, then S is said to be a topological semigroup.
Let E be a Hausdorff topological space
and U an open subset of E.
Recall that a completely regular Hausdorff topological space
X is called Lindelof [SIGMA] (or K-countably determined) if there is an upper semi-continuous compact-valued map T from a non-empty subset [SIGMA] of the product space [N.
Let Top be the site defined by the category of (locally compact) Hausdorff topological spaces
with the open covering Grothendieck topology (as in the "gros topos" of [5, [section]2]).