Definition:Subcontinuum/Proper Subcontinuum

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Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$ be a continuum in $T$.


Let $K$ be a subcontinuum of $H$ such that $K \ne H$.

That is, let $K$ be a proper subset of $H$.


Then $K$ is a proper subcontinuum of $H$.


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