GATE Topology: Topological Spaces and Constructions – Previous Year Questions
9 GATE previous year questions on Topological Spaces and Constructions (Topology, Mathematics) with answers and explanations, from every paper.
- GATE 2021 MA Q24 – On ℝ let T₁=U:0∉U or U=ℝ,T₂=U:0∈U or U=∅,T₃=T₁∩T₂. Find the closure of 1 in (ℝ,T₃).
- GATE 2021 MA Q51 – On ℝ let T₁ be the upper-limit topology with basis (a,b], T₂ the cofinite topology and T₃ the usual topology with basis (a,b). Which inclusion order…
- GATE 2022 MA Q23 – Let p:[0,1]→0,1 be the indicator of [1/2,1], with the usual interval topology and its induced quotient topology on 0,1. Which holds?
- GATE 2024 MA Q13 – For A⊆X in any topological space, write int, ∂ and overbar for interior, boundary and closure. Which inclusion need not hold?
- GATE 2025 MA Q44 – On the unit sphere S⊂ℝ³ identify points exactly when their third coordinates agree. Give the equivalence-class space the quotient topology. To which…
- GATE 2025 MA Q46 – X=ℝ and Y=[0,1], each with the usual distance. In which space is [0,1/4) open?
- GATE 2025 MA Q53 – f:ℝ²→ℝ² is (e2 x2 y,e2 x2 y). Which statements hold?
- GATE 2026 MA Q34 – How many distinct topologies on 1,2,3 have exactly four open sets? (integer)
- GATE 2026 MA Q62 – X=5,6,7,8,9,10 has topology ∅,X,5,6,7,8,9,10. How many subsets are neither open nor closed? (integer)