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Every locally compact group which is second-countable is metrizable as a topological group ( i. e. can be given a left-invariant metric compatible with the topology ) and complete.
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Every and locally
* 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 locally compact space is compactly generated.
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 and 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 and group
Every finite simple group is isomorphic to one of the following groups:
Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.
* Every group G acts on G, i. e. in two natural but essentially different ways:, or.
Every galaxy of sufficient mass in the Local Group has an associated group of globular clusters, and almost every large galaxy surveyed has been found to possess a system of globular clusters.
* 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 instrumental group ( or section ) has a principal who is generally responsible for leading the group and playing orchestral solos.
* Every closed subgroup of a profinite group is itself profinite ; the topology arising from the profiniteness agrees with the subspace topology.
While he admits the existence of caste-based discrimination, he writes that " Every social group cannot be regarded as a race simply because we want to protect it against prejudice and discrimination ".
Every local group is required to have a seneschal who reports to the kingdom's seneschal.
Every local group is required to have one.
* Every topological group is completely regular.
Every summer the group gathers in Newport, RI for week long dance training, seaside teas, and evenings enjoying the splendors of the Gilded Age.
* Every finitely generated group with a recursively enumerable presentation and insoluble word problem is a subgroup of a finitely presented group with insoluble word problem
Every synset contains a group of synonymous words or collocations ( a collocation is a sequence of words that go together to form a specific meaning, such as " car pool "); different senses of a word are in different synsets.
Every group can be trivially made into a topological group by considering it with the discrete topology ; such groups are called discrete groups.
Every topological group can be viewed as a uniform space in two ways ; the left uniformity turns all left multiplications into uniformly continuous maps while the right uniformity turns all right multiplications into uniformly continuous maps.
Every subgroup of a topological group is itself a topological group when given the subspace topology.
:" Every group is naturally isomorphic to its opposite group "
Every ten years, when the general census of population takes place, each citizen has to declare which linguistic group they belong or want to be aggregated to.
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