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Ali Reza
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Existence of an arbitrary Small positive continuous real Valued Function

Let $(X,\tau)$ be a Tychonoff Topological space.

For each $x\in X$ consider an arbitrary positive real number $\epsilon_x>0$. Is There a continuous real valued function $f:X\rightarrow \mathbb{R}$ with the following property:

$$\forall x \in X $$

$$0< f(x) < \epsilon_x$$

Ali Reza
  • 1.8k
  • 10
  • 20