第 22099 題：緊緻集的連續像

原題與已知條件

compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-25,"right":25,"value":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — compact K、完整來源與目標拓撲以及total continuous map。操作=compactimg-reverse-implication-boundary；資料={"left":-25,"right":25,"value":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-continuous-image-of-compact

逐步推導

source operation=compactimg-reverse-implication-boundary;original snapshot and mathematics retained

explicit ordered source output fields=[left, right, constant_value, domain_compact, continuous, image_compact, reverse_implication_claim, boundary]

ORIGINAL WHOLE real interval(-25,25);constant real image value=23

for integers j>=0,relative opens U_j=(L+(R-L)/(j+2),R) cover the interval;ANY finite subfamily is contained in U_max_j and misses a nonempty interval near L,so domain NOT compact

ORIGINAL noncompact domain=(-25,25);constant f(x)=23

preimage of ANY target open is either the whole domain or empty,so continuous;image singleton has a one-member subcover from any cover;reverse implication claim=否

逐步反向核對

• S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。

結論

(-25, 25, 23, 否, 是, 是, 否, constant_continuous_map_from_noncompact_open_interval_has_compact_singleton_image)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。