Definition:Hereditarily Compact Space/Definition 2

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Definition

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


$T$ is hereditarily compact if and only if:

for each family $\family {U_i}_{i \mathop \in I}$ of open sets of $T$, there exists a finite subset $J \subset I$ such that:
$\ds \bigcup_{j \mathop \in J} U_j = \bigcup_{i \mathop \in I} U_i$


Also see


Sources