  We prove that for every normal topological space $X$ and any function $f: X
\to \mathbb{R}$ there is a continuous function $g : X \to \mathbb{R}$ such that
$$|f(x) - g(x)| \leq \frac{1}{2} \sup\limits_{p \in X} \inf\limits_{O(p)}
\sup\limits_{a,b \in O(p)} |f(a) - f(b)|$$ for all $x \in X$.
  As an application of this result we prove the following statements to types
of tightness in a space $Q_p(X, \mathbb{R})$ of all quasicontinuous real-valued
functions with the topology $\tau_p$ of pointwise convergence: the countability
of tightness (fan-tightness, strong fan-tightness) at a point $f$ of space
$Q_p(X, \mathbb{R})$ implies the countability of tightness (fan-tightness,
strong fan-tightness) of space $Q_p(X,Y)$ of all quasicontinuous functions from
$X$ into any non-one-point metrizable space $Y$. This result is the answer to
the open question in the class of metrizable spaces.
