Which of the following statements are true?

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Which of the following statements are true?
1. Any compact topological space is metrizable
2. Any continuous image of a Hausdorff topological space is Hausdorff
3. If f:X Y is continuous and one-to-one, and Y is Hausdorff, then X is
Hausdorff
4. Intersection of two connected subsets of R with the usual topology is either
empty or connected
Transcribed Image Text:Which of the following statements are true? 1. Any compact topological space is metrizable 2. Any continuous image of a Hausdorff topological space is Hausdorff 3. If f:X Y is continuous and one-to-one, and Y is Hausdorff, then X is Hausdorff 4. Intersection of two connected subsets of R with the usual topology is either empty or connected
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