Category:Union of Interiors is Subset of Interior of Union

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This category contains pages concerning Union of Interiors is Subset of Interior of Union:


Let $T$ be a topological space.


Let $\H$ be a set of subsets of $T$.

That is, let $\H \subseteq \powerset T$ where $\powerset T$ is the power set of $T$.


Then the union of the interiors of the elements of $\H$ is a subset of the interior of the union of $\H$:

$\ds \bigcup_{H \mathop \in \H} H^\circ \subseteq \paren {\bigcup_{H \mathop \in \H} H}^\circ $

Pages in category "Union of Interiors is Subset of Interior of Union"

The following 3 pages are in this category, out of 3 total.