सामान्य सांस्थितिकी (usual topology) के साथ ℝ पर विचार कीजिए। निम्नलिखित में से कौन सा कथन सही है?

The topology 𝒯 on the real line ℝ generated by the basis of all closed intervals [d, d+1] of length 1 is ________.

Let (X, τ) be a topological space and (Y, d) be a metric space. If f, g : X → Y are continuous functions, then the set {x ∈ X : f(x) = g(x)} is:

Let X and Y be topological spaces. Consider the statement S: 'For every open subset U ⊆ X × Y and every x ∈ X such that {x} × Y ⊆ U, there exists a neighbourhood W of x in X such that W × Y ⊆ U.' Which of the following conditions guarantees that statement S is true?

Let (X, d1) and (Y, d2) be metric spaces. A function f: X → Y is continuous if and only if:

Which of the following subsets is NOT a connected subset of real numbers (ℜ)?