In _{1}, which is equivalent to the statement that points are closed. Specifically, every weak Hausdorff space is a T_{1} space.
The notion was introduced by M. C. McCord. to remedy an inconvenience of working with the

mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...

, a weak Hausdorff space or weakly Hausdorff space is a topological space
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gener ...

where the image of every continuous map
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

from a compact
Compact as used in politics may refer broadly to a pact
A pact, from Latin ''pactum'' ("something agreed upon"), is a formal agreement. In international relations
International relations (IR), international affairs (IA) or internationa ...

Hausdorff space
In topology
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), ...

into the space is closed. In particular, every Hausdorff space is weak Hausdorff. As a separation property, it is stronger than Tcategory
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Philosophy and general uses
*Categorization
Categorization is the ability and activity to recognize shared features or similarities between the elements of the experience of the world (such as O ...

of Hausdorff spaces. It is often used in tandem with compactly generated space In topology, a compactly generated space (or k-space) is a topological space whose topology is coherent topology, coherent with the family of all compact space, compact subspaces. Specifically, a topological space ''X'' is compactly generated if it ...

s in algebraic topology
Algebraic topology is a branch of mathematics
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.
A Δ-Hausdorff space is a topological space where the image of every path
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Physical paths of different types
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* Bridle path, used by people on horseback
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is closed; i.e. if $f\; :$, 1
The comma is a punctuation
Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...

\to X is continuous, then $f($, 1
The comma is a punctuation
Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, ...

is closed. Every weak Hausdorff space is Δ-Hausdorff, and every Δ-Hausdorff space is T1. A space is Δ-generated, if its topology is the finest such that each map $f\; :\; \backslash Delta^n\; \backslash to\; X$ from a topological n-simplex $\backslash Delta^n$ to $X$ is continuous. Δ-Hausdorff spaces are to Δ-generated spaces as weak Hausdorff spaces are to compactly generated spaces.
See also

*References

Properties of topological spaces {{topology-stub