
die Beachtung
attention
The attention or interest that someone or something receives.
Seine Entdeckung fand in der Fachwelt große Beachtung.
His discovery attracted great attention in the professional community.
attention / observance
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attention
The attention or interest that someone or something receives.
Seine Entdeckung fand in der Fachwelt große Beachtung.
His discovery attracted great attention in the professional community.

observance / compliance
The observance of, or compliance with, rules, laws, or regulations.
Wir bitten um strikte Beachtung der Sicherheitshinweise.
We ask for strict observance of the safety instructions.

to pay no attention
To deliberately ignore someone or something.
Er hat meinen Ratschlägen leider keine Beachtung geschenkt.
Unfortunately, he paid no attention to my advice.
'Beachtung' (attention / observance) is the noun related to the verb 'beachten' (to pay attention to / to observe). The verb 'beachten' means to give something attention or to follow a rule. The noun describes the result or act of doing this.
Bitte beachten Sie die geänderten Öffnungszeiten.
Please note the changed opening hours.
The meaning of 'Beachtung' (attention / observance) depends strongly on the context. In connection with opinions, media, or science, it means 'Aufmerksamkeit' (attention). In the context of rules, laws, and regulations, it means 'Einhaltung' (observance / compliance).
Sein neuer Film fand weltweit Beachtung.
His new film attracted worldwide attention.
In the meaning 'Aufmerksamkeit' (attention), 'Beachtung' is often combined with the verbs 'finden' (to find / to receive) and 'schenken' (to give). You can give someone or something attention, or something can receive attention.
Ihre Arbeit hat in der Forschung große Beachtung gefunden.
Her work has attracted great attention in research.
In the meaning 'Einhaltung' (observance / compliance), 'Beachtung' is often used in formal or official texts. A typical construction is with the genitive or 'von' to say what must be observed.
Die Prüfung muss unter Beachtung der offiziellen Richtlinien erfolgen.
The inspection must be carried out in observance of the official guidelines.
The phrase 'jemandem/etwas keine Beachtung schenken' (to pay no attention to someone/something) means to deliberately ignore someone or something. The person or thing being ignored is in the dative.
Sie hat seinen unhöflichen Kommentaren keine Beachtung geschenkt.
She paid no attention to his rude comments.
attention
Aufmerksamkeit refers to actively directing your thoughts and senses toward something. Beachtung is more about a person or thing being noticed or taken seriously. That is why you give a task your attention, while an important note receives attention.

Der wichtige Hinweis im letzten Abschnitt des Berichts fand bei der Prüferin besondere Beachtung.
The important note in the final section of the report received particular attention from the examiner.
Die Prüferin widmete dem letzten Abschnitt des Berichts besondere Aufmerksamkeit.
The examiner devoted particular attention to the final section of the report.