Chapter 1
neighborhoods, open sets, closed set, etc. We present the definition based on open sets. (Ω, Σ) Definition (via open sets): A topological space is an ordered pair (X, τ), where X is a set and τis a collection of subsets ofX, satisfying: 1. Ø; X ∈τ 2. τis closed under finite intersections. 3. τis closed under arbitrary unions.
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