6:Tf14,

Theorem 7.6. Let $X_n$ be a nonempty finite discrete space for every $n\in\N$ . Then $\prod_{n\in\N}X_n$ is compact.

1:["$","div",null,{"className":"site-shell","children":[["$","a",null,{"className":"skip-link","href":"#site-content","children":"Skip to content"}],["$","header",null,{"className":"site-header","children":[["$","a",null,{"className":"site-title","href":"/","aria-label":"FPRD Lab home","children":"FPRD Lab"}],["$","nav",null,{"aria-label":"Primary navigation","children":[["$","a","/research-programs",{"aria-current":"$undefined","href":"/research-programs","children":"Research"}],["$","a","/claims",{"aria-current":"$undefined","href":"/claims","children":"Claims"}],["$","a","/philosophy",{"aria-current":"$undefined","href":"/philosophy","children":"Philosophy"}],["$","a","/publications",{"aria-current":"$undefined","href":"/publications","children":"Publications"}]]}],["$","a",null,{"className":"community-link","href":"/philosophy#other-approaches","children":"Share an approach"}]]}],["$","div",null,{"id":"site-content","tabIndex":-1,"children":["$","main",null,{"className":"theorem-page","children":[["$","nav",null,{"className":"document-toolbar","aria-label":"Theorem resources","children":[["$","a",null,{"href":"/theorems","children":"← Theorem library"}],["$","span",null,{"children":"theorem"}],["$","span",null,{"children":["released"," publication"]}],["$","a",null,{"href":"/publications/fprd-program-textbook#siteauto:chapters-07-products-compactness-tex:6","children":"Read in publication"}],["$","a",null,{"href":"/library/publications/fprd-program-textbook/fprd-program-textbook.pdf","children":"PDF"}]]}],["$","article",null,{"className":"theorem-entry-page","children":[["$","header",null,{"children":[["$","p",null,{"className":"eyebrow","children":"theorem"}],["$","h1",null,{"children":"Theorem 7.6"}],null]}],["$","article",null,{"className":"theorem-statement-document","dangerouslySetInnerHTML":{"__html":"$6"}}],"$L7"]}]]}]}],"$L8"]}] 7:["$","aside",null,{"className":"theorem-source-note","children":[["$","strong",null,{"children":"Publication context"}],["$","p",null,{"children":["This statement is reproduced from"," ",["$","a",null,{"href":"/publications/fprd-program-textbook#siteauto:chapters-07-products-compactness-tex:6","children":"FPRD program textbook"}],". Read it there for the surrounding definitions, proof, citations, and limitations."]}]]}] 8:["$","footer",null,{"className":"site-footer","children":[["$","p",null,{"className":"site-footer-disclosure","children":[["$","strong",null,{"children":"Research status:"}]," FPRD Lab is largely AI-driven. Its work has not been reviewed by qualified mathematicians. "," ",["$","a",null,{"href":"/about#research-status","children":"Details"}],"."]}],["$","p",null,{"children":"Exploring mathematics, sharing what we learn. Our practice is open to correction."}],["$","p",null,{"children":["Directed and maintained by Joshua Gay ·"," ",["$","a",null,{"href":"mailto:joshuagay@gmail.com","children":"joshuagay@gmail.com"}]]}],["$","p",null,{"children":["Foundational library snapshot"," ",["$","a",null,{"href":"https://gitlab.com/insight-forge/boxlab/fprd-lab/-/commit/3a264faa095a3afb3269c500b4ed7400d6402d65","rel":"noreferrer","target":"_blank","children":"3a264faa09"}]," ","· ","2026-08-25"]}]]}]