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* Every locally compact regular space is completely regular, and therefore every locally compact Hausdorff space is Tychonoff.
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Every and locally
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 regular
Every regular language is context-free, every context-free language, not containing the empty string, is context-sensitive and every context-sensitive language is recursive and every recursive language is recursively enumerable.
Every regular ordinal is the initial ordinal of a cardinal.
* Every regular language is context-free because it can be described by a context-free grammar.
* Every metric space is Tychonoff ; every pseudometric space is completely regular.
* Every topological group is completely regular.
* Every normal regular space is completely regular, and every normal Hausdorff space is Tychonoff.
* Every subspace of a completely regular or Tychonoff space has the same property.
* Every Borel set E is outer regular:
* Every open set E is inner regular:
Every such space is regular.
Nordau saw in Jewish Emancipation the result of ' a regular equation: Every man is born with certain rights ; the Jews are human beings, consequently the Jews are born to own the rights of man.
Every regular map of varieties is continuous in the Zariski topology.
Every such regular cover is a principal G-bundle, where G = Aut ( p ) is considered as a discrete topological group.
Every universal cover p: D → X is regular, with deck transformation group being isomorphic to the fundamental group.
Every fourth year when the games were also held, the festival was known as the " Great Panathenaia ," and was 3 or 4 days longer than the regular festival.
“ Every three months ( after regular cleaning ) the wheels should be coated with petroleum jelly .”
Every US President since Roosevelt has delivered a regular address.
Every polyhedron, regular and irregular, convex and concave, has a dihedral angle at every edge.
Every extremal monomorphism is regular.
Every extremal epimorphism is regular.
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