MTH634 quiz no 3 2022 solution by taleemi markaz part 1

MTH634 Quiz No.3 Part 1 with 100% accurate Solution. For More Parts Click The Links Given below: Part 1    • MTH634 quiz no 3 2022 solution by taleemi ...   Part 2 Coming Soon #MTH634Quiz3 #mth634finalquiz #mth634 #mth634finalterm #Topology For More Quiz Keep visiting our Channel "TALEEMI MARKAZ". Don't Forget to Subscribe our Channel. Thanks Quiz: Metric topology induced by 𝒅(𝒙,𝒚)={■8(𝟎 𝒊𝒇 𝒙=𝒚@𝟏 𝒊𝒇 𝒙≠𝒚)┤ is called Metric topology induced by 𝒅(𝒙,𝒚)=|𝒙−𝒚| on ℝ is called Which of the following statement is true? Every metric space is first countable. Let 𝑿={𝟏,𝟐,𝟑,𝟒,𝟓,𝟔} and 𝝉={∅,{𝟏},{𝟐},{𝟏,𝟐},𝑿} be a topology on 𝑿, then the local base (𝑩_𝒙) of the point 𝒙=𝟏 is ________ Let 𝑿={𝟏,𝟐,𝟑,𝟒,𝟓,𝟔} and 𝝉={∅,{𝟏},{𝟐},{𝟏,𝟐},𝑿} be a topology on 𝑿, then the local base (𝑩_𝒙) of the point 𝒙=𝟐 is ________ Let 𝑿={𝟏,𝟐,𝟑,𝟒,𝟓,𝟔} and 𝝉={∅,{𝟑},{𝟒},{𝟑,𝟒},𝑿} be a topology on 𝑿, then which of the following is true? Let 𝑿={𝟏,𝟐,𝟑,𝟒,𝟓,𝟔} and 𝝉={∅,{𝟑},{𝟒},{𝟑,𝟒},𝑿} be a topology on 𝑿, then which of the following is true? Every topological space is first countable. Which of the following statement is false?