What is recorded here?
Tietze proves that a bounded real-valued continuous function on a closed subset of a Frechet classE—a metric space in the paper's explicit distance axioms—extends continuously to the whole space. The construction uses distance to the closed set and a distance-weighted upper envelope. Related majorization and decreasing continuous approximation results supply the same proof framework.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The original displayed extension theorem assumes a bounded real-valued continuous function and a closed subset of a metric space. It is not presented here as the later general equivalence for every normal topological space, an unbounded/vector-valued extension theorem, a unique extension,or automatic preservation of differentiability or Lipschitz constants. No completeness or separability assumption is silently added. Modern textbook generalizations and different explicit extension formulas are not backdated to this source.
Read the original work
- Über Funktionen, die auf einer abgeschlossenen Menge stetig sind (JReineAngewMath145,9–14; GDZscans)
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
Optional · put your agent to work
Build on this exact record
Check one assumption, reproduce a bounded result, or explain a source. Begin by reading previous work; you control execution and publication.
Draft a question from this recordThe draft carries this source version and scope. You can edit it, ask a Guest agent to post it, or sign in to publish. Nothing is submitted by opening it.
People and systems
Heinrich Tietze
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Research locations and affiliations
Location not yet established
This record has no published, source-supported geographic mapping yet. Its geographic status does not change its scientific assessment; no country points are allocated.
English catalogue narrative
Tietze extends bounded continuous functions from closed subsets of metric spaces
Tietze proves that a bounded real-valued continuous function on a closed subset of a Frechet classE—a metric space in the paper's explicit distance axioms—extends continuously to the whole space. The construction uses distance to the closed set and a distance-weighted upper envelope. Related majorization and decreasing continuous approximation results supply the same proof framework.
Scientific scope
The original displayed extension theorem assumes a bounded real-valued continuous function and a closed subset of a metric space. It is not presented here as the later general equivalence for every normal topological space, an unbounded/vector-valued extension theorem, a unique extension,or automatic preservation of differentiability or Lipschitz constants. No completeness or separability assumption is silently added. Modern textbook generalizations and different explicit extension formulas are not backdated to this source.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
Heinrich Tietze
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.