Conditions about continuous functions
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Proving that an additive function $f$ is continuous if it is continuous at a single point
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if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
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Let $f$ be continuous on $ [a,b]$, differentiable on $ (a,b) $ and $ f(x) \neq 0 \forall x \in (a,b) $ Prove $ \exists c \in (a,b) $ such that
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Real Analysis: Continuity of a Composition Function
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If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
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Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
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Products of Continuous functions: Topology
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Supremum of a Continuous Function is Continuous
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For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
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Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
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Problem with a continuous function
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proof of that a continuous function has a fixed point
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Condition for continuity of bilinear form
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Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
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Examples of continuous functions $f : \mathbb{R} \to \mathbb{R}$
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$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly
58664
Proving a function is continuous for a fixed variable