Carter, Sheila2021-07-302021-07-301994Carter, S. ve Ezentaş, R. (1994). ''Embeddings of nonorientable surfaces with totally reducible focal set''. Glasgow Mathematical Journal, 36(1), 11-16.0017-0895https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3BD7D3D61EDA038B110DBD2EE4BE9A01/S0017089500030494a.pdf/div-class-title-embeddings-of-nonorientable-surfaces-with-totally-reducible-focal-set-div.pdfhttps://doi.org/10.1017/S0017089500030494http://hdl.handle.net/11452/21333In an earlier paper [5] we introduced the idea of an immersion f:M W with totally reducible focal set.Such an immersion has the property that, for all peM, the focal set with base p is a union of hyperplanes in the normal plane to f(M) at .Trivially, this always holds if n=m+1 so we only consider n > m + 1.In [5] we showed that if M2 is a compact surface then for all n>4 there is a substantial immersion:A/2 R with totally reducible focal set. Further, if M2 is orientable or is a Klein bottle or a Klein bottle with handles then/:M2 W can be taken to be an embedding.Here we show that if M2 is a projective plane or a projective plane with handles then for all 5 there exists a substantial embedding f:M2 M with totally reducible focal set although,by arguments of M. Gromov and E. G. Rees,for n=4 such an embedding does not exist.eninfo:eu-repo/semantics/openAccessMathematicsOrientation of surfacesUnverified surfacesArticleA1994NB197000022-s2.0-849740981341116361Mathematics