* Every uniform isomorphism and isometric isomorphism is a homeomorphism.

Every homeomorphism is a homotopy equivalence, but the converse is not true: for example, a solid disk is not homeomorphic to a single point, although the disk and the point are homotopy equivalent.

Every local homeomorphism is a continuous and open map.

* Every cover is a local homeomorphism — that is, for every, there exists a neighborhood of c and a neighborhood of such that the restriction of p to U yields a homeomorphism from U to V. This implies that C and X share all local properties.

* Every local diffeomorphism is also a local homeomorphism and therefore an open map.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every single problem touched on thus far is related to good marketing planning.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

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

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

Every night they all went to Mama and Papa Albright's, and sat on the open front porch, where they could get the breeze.

# Every open cover of A has a finite subcover.

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

When coming to Kubla Khan, he pointed out: " instead of being content to have written finely under the influence of laudanum, recommends ' Kubla-Khan ' to his readers, not as a poem, but as ' a psychological curiosity ' ... Every lover of books, scholar or not, who knows what it is to have his quarto open against a loaf at his tea ... ought to be in possession of Mr. Coleridge's poems, if it is only for ' Christabel ', ' Kubla Khan ', and the ' Ancient Mariner '.

Every island has sand beaches, but few open onto spacious lowlands.

Every judgment contained the reasons behind the decision and the judges assenting ; if there was a dissenting judge, he was allowed to deliver his own judgment, with all judgments read in open court before the agents of the parties to the dispute.

* Every open set E is inner regular:

Every day, doors seem to open, and every day, we interact, perhaps more than ever before, with the world outside.

Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G

Every organization using oscilloscopes has a wide variety of calibration approaches open to them.

* Every closed nowhere dense set is the boundary of an open set.

Every map that is injective, continuous and either open or closed is an embedding ; however there are also embeddings which are neither open nor closed.

Every year, Eton employs a ' Director-in-Residence ', an external professional director on a one-year contract who normally directs one house play and the Lower Boy play ( a school play open solely to the first two year groups ), as well as teaching Drama and Theatre Studies to most year groups.

Every microwave oven sold has a protective interlock so that it cannot be run when the door is open or improperly latched.

Every Tuesday and Saturday mornings in the summer near the old train station a farmers ' market is open, where farmers sell their fresh goods.

Every week of the Michaelmas and Lent terms, and twice in Easter term, Churchill is host to Pav, a music event unusual for Cambridge events in that it is free and open to all university members.

Every mRNA consists of three parts-5 ' untranslated region ( 5 ' UTR ), protein-coding region or open reading frame ( ORF ) and 3 ' untranslated region ( 3 ' UTR ).

Every smooth manifold defined in this way has a natural diffeology, for which the plots correspond to the smooth maps from open subsets of R < sup > n </ sup > to the manifold.

Every May, the community honors him with the open air Django Reinhardt Jazz Festival.

* Every subset of Baire space or Cantor space is an open set in the usual topology on the space.

Every summer, operas, music and drama are performed in the open air at the Freilichtbühne during the month-long Wetzlar Festival (" Wetzlarer Festspiele ").

Every year there is a famous cross-country ski race called the Engadin Skimarathon from Maloja, across the frozen lakes and over the open meadows and ending in S-chanf.