Let f : [K.sub.1] [right arrow] [K.sub.2] be a singlevalued neutrosophic soft continuous
surjective function. If [mathematical expression not reproducible] is a single-valued neutrosophic soft [C.sub.5]-connected space, then [mathematical expression not reproducible] is also single-valued neutrosophic soft [C.sub.5]-connected.
A topological space (X, [tau]) is [[alpha].sup.[gamma]]-[D.sub.1] if for each pair of distinct points x, y [member of] X, there exists an [[alpha].sup.([gamma],[beta])]-irresolute
surjective function f: (X, [tau]) [right arrow] (Y, [sigma]), where Y is an [[alpha].sup.[beta]]-[D.sub.1] space such that f(x) and f(y) are distinct.
X is vg-[D.sub.1] iff for each x [not equal to] y [member of] X, [there exists]vg-irresolute
surjective function f, where Y is a vg-[D.sub.1] space [contains as member] f(x) [not equal to] f(y).
If g: X [right arrow] Y is a sg-continuous quasi sg-closed
surjective function, then Y is normal.
By hypothesis, [there exists] a rg[alpha]--irresolute,
surjective function f from X onto a rg[alpha] - [D.sub.1] space Y such that f(x) [not equal to] f(y).
By hypothesis, there exists a g-irresolute,
surjective function f of a space X onto a g - [D.sub.1] space Y such that f(x) [not equal to] f(y).
of span(C) is continuous and surjective, since it is the composition of continuous
surjective functions (recall that, from Lemma 2.4, [[summation].sup.l.sub.i = 1] [[lambda].sub.i] [F.sub.i] is a continuous
surjective function).
In [8] Aron and Seoane-Sepulveda showed that there exists an infinitely generated algebra in the set of everywhere
surjective functions on C.
In this case, it is immediate to see that SkY[T.sub.0] (n, k) is in bijection with all
surjective functions from an n-set to a k-set: just interpret the elements of a tableau as balls and the rows of a tableau as boxes.
Seoane-Sepiilveda, Uncountably generated algebras of everywhere
surjective functions, Bull.
Gamez-Merino, Large algebraic structures inside the set of
surjective functions, Bull.