Topology-1

1. Topological space satisfying the T_2 separation axiom
4. Subset of top. space X that is the union of a countable collection of nowhere dense subsets in X
5. Said of a topology with the property that arbitrary intersections of open sets are open
7. Both connected and compact sets
8. A separable and completely metrizable space
11. Space having a countable dense subset
13. Space that contains no non-empty dense-in-itself subset
14. Space X such that any continuous real-valued function on X is bounded
16. Largest open subset of a non-empty connected compact space
17. Space such that any open cover has a countable subcover
18. Space such that the intersection of countable dense open sets is dense
20. Set with no disjoint open sets

2. Space satisfying the T_0 and T_3 separation axioms
3. Space such that any open cover has an open locally finite refinement
6. Developable regular Hausdorff space
7. Said of the continuous image of separable metric spaces
9. Closed and dense-in-itself space
10. Space such that any open cover possesses an interior-preserving refinement
12. Locally connected generalized continua containing no closed simple curve
15. Property that states that any collection of non-empty open and disjoint sets is at most countable
19. Showed that a countable paracompact and normal space Y is equivalent to Yx[0,1] being normal