Category:Continuous Mappings into Hausdorff Space coinciding on Everywhere Dense Set coincide
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This category contains pages concerning Continuous Mappings into Hausdorff Space coinciding on Everywhere Dense Set coincide:
Let $\struct {X, \tau_X}$ be a topological space.
Let $\struct {Y, \tau_Y}$ be a Hausdorff space.
Let $D$ be an everywhere dense subset of $X$.
Let $f : X \to Y$ and $g : X \to Y$ be continuous mappings such that:
- $\map f x = \map g x$ for all $x \in D$.
Then:
- $\map f x = \map g x$ for all $x \in X$.
Pages in category "Continuous Mappings into Hausdorff Space coinciding on Everywhere Dense Set coincide"
The following 2 pages are in this category, out of 2 total.