* Every locally compact regular space is completely regular, and therefore every locally compact Hausdorff space is Tychonoff.

Every compact Hausdorff space is also locally compact, and many examples of compact spaces may be found in the article compact space.

Every regular space is locally regular, but the converse is not true.

*( BCT2 ) Every locally compact Hausdorff space is a Baire space.

* Roslyn Sunday Market – Every Sunday from June through September, this outdoor farmer's market and craft fair is located on Pennsylvania Avenue in downtown Roslyn and offers a selection of local fruits, vegetables, arts, crafts and locally produced specialty items.

*( BCT2 ) Every locally compact Hausdorff space is a Baire space.

Every constant function is locally constant.

Every locally constant function from the real numbers R to R is constant by the connectedness of R. But the function f from the rationals Q to R, defined by f ( x ) = 0 for x < π, and f ( x ) = 1 for x > π, is locally constant ( here we use the fact that π is irrational and that therefore the two sets

* Every cyclic group is locally cyclic, and every locally cyclic group is abelian.

* Every finitely-generated locally cyclic group is cyclic.

* Every subgroup and quotient group of a locally cyclic group is locally cyclic.

: Every correspondence that maps a compact convex subset of a locally convex space into itself with a closed graph and convex nonempty images has a fixed point.

Every year ; on the Sunday after Easter, the village holds a Brawn eating competition ( known locally as Pork Cheese ).

Every year Exhibition ( Mela ) locally called as ' Urus ' takes place.

Every October is " Apple Day " when the apples are harvested from locally owned orchards.

Every Friday of the year is locally known as Quiapo Day, and is dedicated to the Black Nazarene, with the novena being held not only in the basilica but in other churches nationwide.

Every Monday, Wednesday and Saturday a lively open air market was held featuring fresh locally raised produce, poultry and locally crafted artefacts.

Every closed subgroup of a locally compact group is locally compact.

* Every topological space X is a dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification.

* Every compact metric space is separable.

* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.

* Sequentially compact: Every sequence has a convergent subsequence.

* Countably compact: Every countable open cover has a finite subcover.

* Limit point compact: Every infinite subset has an accumulation point.

Every compact metric space is complete, though complete spaces need not be compact.

Every entire function can be represented as a power series that converges uniformly on compact sets.

* Every compact metric space ( or metrizable space ) is separable.

Every Tychonoff cube is compact Hausdorff as a consequence of Tychonoff's theorem.

Every continuous function on a compact set is uniformly continuous.

* Every compact Hausdorff space of weight at most ( see Aleph number ) is the continuous image of ( this does not need the continuum hypothesis, but is less interesting in its absence ).

Every group has a presentation, and in fact many different presentations ; a presentation is often the most compact way of describing the structure of the group.

Every H * is very special in structure: it is pure-injective ( also called algebraically compact ), which says more or less that solving equations in H * is relatively straightforward.

** Every vector space has a basis.

** Every infinite game in which is a Borel subset of Baire space is determined.

** Every Tychonoff space has a Stone – Čech compactification.

* Theorem Every reflexive normed space is a Banach space.

Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

* Pseudocompact: Every real-valued continuous function on the space is bounded.

Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.

Every point in three-dimensional Euclidean space is determined by three coordinates.

Every node on the Freenet network contributes storage space to hold files, and bandwidth that it uses to route requests from its peers.

Every space filling curve hits some points multiple times, and does not have a continuous inverse.

* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )

Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.

Every normed vector space V sits as a dense subspace inside a Banach space ; this Banach space is essentially uniquely defined by V and is called the completion of V.