Question

For Topology!!!

Match the terms and phrases below with their definitions. X and Y represents topological spaces. Note: there are more terms than definitions! Terms: compact, connected, Hausdorff, homeomorphis, quotient topology, discrete topology, indiscrete topology, open set continuous, closed set, open set, topological property, separation, open cover, finite refinement, B(1,8) 20. A collection of open subsets of X whose union equals X 20. 21. The complement of an open set 21. 22. Distinct points r and y can be separated by open sets U containing r, V containing y, with 22. 23. A continuous bijection bet ween topological spaces with a contiuous inverse. 23. 24. A characteristic of a topological space defined purely in terms of open sets 24. 25. In a metric space, the set of points whose distance from some given point is bounded by some nonzero constant. 25. 26. A pair of nonempty, open, disjoint sets whose union equals X 26. 27. A subset of an open cover having finitely many open sets whose union equals X 27. 28. The topology on X/~whereis an equivalence relation on X. 28. 29. A function f : X → Y satisfying U open in Y implies f-1(U) is open in X. 29. 30. A topology on X equivalent to the power et P(x) 30.

Answer 1

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