*Definition [#yf2a7df1]
-A topological space X is called locally compact if every point of X has a [[compact]] neighbourhood.

*Property [#t3ca1fb5]
-Every locally compact Hausdorff space is [[Tikhonov]].
-Every locally compact, [[paracompact]] Hausdorff space is [[strongly paracompact]].
-For every compact subspace A of a locally compact space X and every open set V that contains A there exists an open set U such that &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20A%5csubset%20U%5csubset%20%5coverline%7bU%7d%5csubset%20V%20and%5c%20%5coverline%7bU%7d%20%5c%5d%7d%25.png); is compact.
-If X is locally compact space, then every subspace of X that can be represented in the form F∩V, where F is closed in X and V is open in X, also is locally compact.
-Every locally compact subspace M of a Hausdorff space X is an open subset of the closure of the set M in the space X, i.e., it can be represented in the form F∩V, where F is closed in X and V is open in X.
-The sum &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cbigoplus%7b%7d_%7bs%5cin%20S%7d%20X_s%20%5c%5d%7d%25.png); is locally compact if and only if all spaces X_s are locally compact.
-The Cartesian product &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cprod%7b%7d_%7bs%5cin%20S%7d%20X_s%20%5c%5d%7d%25.png); , where &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20X_s%5cneq%5cemptyset%5c%20%5ctext%7bfor%7d%5c%20s%5cin%20S%20%5c%5d%7d%25.png);, is locally compact if and only if all spaces X_s are locally compact and there exists a finite set &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20S_0%5csubset%20S%20%5c%5d%7d%25.png); such that X_s is compact for &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20s%5cin%20S%5cbackslash%20S_0%20%5c%5d%7d%25.png);.
-If there exists on open mapping f:X→Y of a locally compact space X onto a Hausdorff space Y, then Y is a locally compact space.
-For every locally compact space X and any quotient mapping g:Y→Z, the Cartesian product f=Id_X×g;X×Y→X×Z is a quotient mapping.
-If X is locally compact, then for every topological space Y the compact-open topology on Y^X is acceptable.
-Every locally compact [[paracompact]] space X can be represented as the union of a family of disjoint closed-and-open subspaces of X each of which has the [[Lindeloef]] property.
-Every non-empty hereditarily disconnected locally compact space is zero-dimensional.
-Hereditary disconnectedness, zero-dimensionality and strong zero-dimensionality are equivalent in the realm of non-empty locally compact [[paracompact]] spaces.
-For every non-emty locally compact [[paracompact]] space X the conditions ind X=0, Ind X=0 and dim X=0 are equivalent to hereditary disconnectedness of X.
-a [[coarsest uniformity]] on a [[Tykhonov]] space X exists if and only if the space X is locally compact.
-Every locally compact preregular space is completely regular.
-Every locally compact Hausdorff space is a Baire space.
-A subspace X of a locally compact Hausdorff space Y is locally compact if and only if X can be written as the set-theoretic difference of two closed subsets of Y. 
*Reference [#l6232aa1]
John L. Kelley, ''General Topology'', Springer (1975).