{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T05:38:00Z","timestamp":1648618680304},"reference-count":9,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2007]]},"abstract":"<jats:p>A point<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>p<\/mml:mi><\/mml:math>of a topological space<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>X<\/mml:mi><\/mml:math>is a cut point of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>X<\/mml:mi><\/mml:math>if<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>X<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:mrow><mml:mo>{<\/mml:mo><mml:mi>p<\/mml:mi><mml:mo>}<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>is disconnected. Further, if<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>X<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:mrow><mml:mo>{<\/mml:mo><mml:mi>p<\/mml:mi><mml:mo>}<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>has precisely<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>m<\/mml:mi><\/mml:math>components for some natural number<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>m<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:math>we will say that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>p<\/mml:mi><\/mml:math>has cut point order<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>m<\/mml:mi><\/mml:math>. If each point<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>y<\/mml:mi><\/mml:math>of a connected space<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>Y<\/mml:mi><\/mml:math>is a cut point of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>Y<\/mml:mi><\/mml:math>, we will say that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>Y<\/mml:mi><\/mml:math>is a cut point space. Herein we construct a space<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>S<\/mml:mi><\/mml:math>so that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>S<\/mml:mi><\/mml:math>is a connected Hausdorff space and each point of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>S<\/mml:mi><\/mml:math>is a cut point of order three. We also note that there is no uncountable separable cut point space with each point a cut point of order three and therefore no such space may be embedded in a Euclidean space.<\/jats:p>","DOI":"10.1155\/2007\/10679","type":"journal-article","created":{"date-parts":[[2007,9,5]],"date-time":"2007-09-05T08:07:45Z","timestamp":1188979665000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Concerning Cut Point Spaces of Order Three"],"prefix":"10.1155","volume":"2007","author":[{"given":"D.","family":"Daniel","sequence":"first","affiliation":[]},{"given":"William S.","family":"Mahavier","sequence":"additional","affiliation":[]}],"member":"98","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.2307\/1989086"},{"key":"2","series-title":"American Mathematical Society Colloquium Publications, Vol. 28","volume-title":"Analytic Topology","year":"1963"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.61.2.380"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-41.3.191"},{"key":"7","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1112\/jlms\/2.Part_4.589","volume":"2","year":"1970","journal-title":"Journal of the London Mathematical Society"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-7.2.199"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-99-04839-X"},{"key":"10","volume-title":"Topology. Vol. II","year":"1968"},{"key":"11","first-page":"1524","volume":"8","year":"1967","journal-title":"Soviet Mathematics Doklady"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2007\/010679.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2007\/010679.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,17]],"date-time":"2017-06-17T22:35:29Z","timestamp":1497738929000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2007\/010679\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"references-count":9,"alternative-id":["010679","10679"],"URL":"https:\/\/doi.org\/10.1155\/2007\/10679","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007]]}}}