Math Chapter Wise

EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q41.Let X = [–1,1] ×[–1,1], A={(x,y) ∈X:x2 +y2 =1}, B={(x,y) ∈ X: x + y = 1}, C={(x,y) ∈X:xy=0},

AA is homeomorphic to B BB is homeomorphic to C CC is homeomprphic to A DNone of the above

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q42.What does the Tychnoff theorem

AProduct of connected spaces is connected BProduct of Housdorff spaces is Housdorff CProduct of compact space is compact DProduct of normal spaces is normal

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q43.Let (X,J) be a topological space, where X={1,2,3} and { } φ J =,{1},{2},{1,2},X A function X → f: X defined by f(1)=3, f(2)=1, f(3)=2 is-

AContinuous at 1 BContinuous at 2 CContinuous at 3 DNone of the above

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q44.Let (X,T) be a topological space, where X={a,b,c} and T= φ {,{a},{b,c},X} then (X,T) is

Aregular and T3 both Bregular but not T3 Cnot regular but T3 Dneither regular nor T3

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q45.Let X={a,b,c} and T={ } φ,{a},{b,c},X is topology on 'X', then which of the following in incorrect?

A{a} is T-closed set B{a} is T- open set C{b,c} is T- closed set DNone of the above

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q46.Which of the following property is not hereditary in a topological space?

ARegularity BHousdroff property CNormality DNone of the above

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EnglishUPPSC GDC 2021

Q47.Which of the following statements is/are true? I: Union of two topologies on X is always a topology on X. II: Intersection of two topologies on X is always a topology on X.

AOnly I BOnly II CBoth I and II DNeither I nor II

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q48.In which condition T is not disconnected?

AT has a decomposition into two nonempty closed sets Bthe only decompositions of T into open sets are T=∅ ∪ T and T = T ∪ ∅ CT has a decomposition into two nonempty open sets DT has a subset which is open, closed and is neither ∅ nor T

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q49.Find out the incorrect statement for the interiors of A and B given by Aº and Bº in (X, d)?

AA ⊆ B →Aº/⊆ Bº BAº ∪ Bº = (A∪B)º CAº ∩ Bº ⊆ (A∪B)º DAº ∩ Bº = (A∩B)º

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q50.The Metric space is both complete and totally bounded is known as ____

ACompact BComplete CScalar DDiscrete

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q51.If d1, d2 are two metrics on the same set M, Which statement is not equivalent from the following statements:

AFor every metric space (N,d), every F: M → N is d1 continuous iff it is d2 continuous Bd1 open and d2 open sets coincide CFor every metric space (N,d), every g: N →M is d1 continuous iff it is d2 continuous. Dthe union of any finite collection of closed sets is closed

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q52.We call a topological space T sequentially compact if_______

AIf T is compact, s∈S and U is an open cover of T × S, there is open V⊂ S containing s such that T × V can be covered by a finite subfamily of U BT is not compact, it has a maximal open cover V without a finite subcover. Cevery sequence in T has a convergent subsequence DU be the collection of their complements. By De Morgan's rules, U is a cover of T.

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EnglishRajasthan TGT 2015

Q53.If (X,d) is a metric space and A,B∈X, then the correct statement is-

AA is an open set. BA is closed if and only if is A A = CA B A B/∪ ≠ ∪ DA B A B/∪ ≠ ∩

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q54.Which of the following define a metric on R?

A() 2 2 d x, y x y = − B() d x, y x 2y = − C() x y d x, y 1 x y − = + − Dnone of these

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