{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T13:23:18Z","timestamp":1769088198440,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T00:00:00Z","timestamp":1555545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we prove the identity       dim   H   ( F )  = d \u00b7   dim   H   (  \u03b1  \u2212 1    ( F )  )     , where      dim   H     denotes Hausdorff dimension,     F \u2286  R d     , and     \u03b1 :  [ 0 , 1 ]  \u2192   [ 0 , 1 ]  d      is a function whose constructive definition is addressed from the viewpoint of the powerful concept of a fractal structure. Such a result stands particularly from some other results stated in a more general setting. Thus, Hausdorff dimension of higher dimensional subsets can be calculated from Hausdorff dimension of 1-dimensional subsets of     [ 0 , 1 ]    . As a consequence, Hausdorff dimension becomes available to deal with the effective calculation of the fractal dimension in applications by applying a procedure contributed by the authors in previous works. It is also worth pointing out that our results generalize both Skubalska-Rafaj\u0142owicz and Garc\u00eda-Mora-Redtwitz theorems.<\/jats:p>","DOI":"10.3390\/sym11040564","type":"journal-article","created":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T11:58:21Z","timestamp":1555588701000},"page":"564","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Calculating Hausdorff Dimension in Higher Dimensional Spaces"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6291-9205","authenticated-orcid":false,"given":"Manuel","family":"Fern\u00e1ndez-Mart\u00ednez","sequence":"first","affiliation":[{"name":"University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720 Santiago de la Ribera, Murcia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2788-809X","authenticated-orcid":false,"given":"Juan Luis","family":"Garc\u00eda Guirao","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada y Estad\u00edstica, Universidad Polit\u00e9cnica de Cartagena, Hospital de Marina, 30203 Cartagena, Murcia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9153-8321","authenticated-orcid":false,"given":"Miguel \u00c1ngel","family":"S\u00e1nchez-Granero","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Almer\u00eda, 04120 La Ca\u00f1ada de San Urbano, Almer\u00eda, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.21042\/AMNS.2018.1.00002","article-title":"A global solution for a reaction-diffusion equation on bounded domains","volume":"3","author":"Khellat","year":"2018","journal-title":"Appl. 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