H
- Hausdorff
- A Hausdorff space (or T2 space) is one in which every two distinct points have disjoint neighbourhoods. Every Hausdorff space is T1.
- H-closed
- A space is H-closed, or Hausdorff closed or absolutely closed, if it is closed in every Hausdorff space containing it.
- Hereditarily P
- A space is hereditarily P for some property P if every subspace is also P.
- Hereditary
- A property of spaces is said to be hereditary if whenever a space has that property, then so does every subspace of it. For example, second-countability is a hereditary property.
- Homeomorphism
- If X and Y are spaces, a homeomorphism from X to Y is a bijective function f : X → Y such that f and f−1 are continuous. The spaces X and Y are then said to be homeomorphic. From the standpoint of topology, homeomorphic spaces are identical.
- Homogeneous
- A space X is homogeneous if, for every x and y in X, there is a homeomorphism f : X → X such that f(x) = y. Intuitively, the space looks the same at every point. Every topological group is homogeneous.
- Homotopic maps
- Two continuous maps f, g : X → Y are homotopic (in Y) if there is a continuous map H : X × → Y such that H(x, 0) = f(x) and H(x, 1) = g(x) for all x in X. Here, X × is given the product topology. The function H is called a homotopy (in Y) between f and g.
- Homotopy
- See Homotopic maps.
- Hyper-connected
- A space is hyper-connected if no two non-empty open sets are disjoint Every hyper-connected space is connected.
Read more about this topic: Glossary Of Topology