Artículos científicos
Publicado 2018-12-12
Palabras clave
- Continuo,
- hiperespacios,
- propiedad b),
- unicoherencia,
- cono
- suspensión ...Más
Cómo citar
Anaya, J. G., Maya, D., & Fuentes-Montes de Oca, A. (2018). Reseña de la búsqueda de hacer agujeros. Revista Integración, Temas De matemáticas, 36(2), 101–116. https://doi.org/10.18273/revint.v36n2-2018003
Resumen
Un espacio topológico conexo Z es unicoherente si para cualesquiera A y B cerrados y conexos de Z, tales que Z = A ∪ B, se tiene que A ∩ B es conexa. Sea Z un espacio unicoherente: decimos que z ∈ Z agujera a Z si Z − {z} no es unicoherente. Un problema de reciente estudio es: dado un espacio topológico unicoherente H(Z), obtenido de un espacio topológico Z, ¿cuáles elementos A ∈ H(Z) lo agujerean? Este trabajo consiste en dar una reseña de los resultados que hasta la fecha se conocen de este problema.
Descargas
Los datos de descargas todavía no están disponibles.
Referencias
[1] Anaya J.G., “Making holes in hyperspaces”, Topology Appl. 154 (2007), 2000–2008.
[2] Anaya J.G., “Making holes in the hyperspaces of a Peano continuum”, Topology Proc. 37 (2011), 1–14.
[3] Anaya J.G., Carranza R.I., Maya D. and Orozco-Zitli F., “Making holes in the hyperspace of subcontinua of smooth dendroids”, Preprint.
[4] Anaya J.G., Castañeda-Alvarado E. and Orozco-Zitli F., “Making holes in the hyperspace of subcontinua of some continua”, Adv. in Pure Math. 2 (2012), 133–138.
[5] Anaya J.G., Castañeda-Alvarado E., Fuentes-Montes de Oca A. and Orozco-Zitli F., “Making holes in the cone, suspension and hyperspaces of some continua”, Comment. Math. Univ. Carolin. 59 (2018), No. 3, 343–364.
[6] Anaya J.G., Castañeda-Alvarado E., Fuentes-Montes de Oca A. and Orozco-Zitli F., “Making holes in the hyperspaces suspension of some continua”, Preprint.
[7] Anaya J.G., Maya D. y Orozco-Zitli F., “Agujeros en el segundo producto simétrico de subcontinuos del continuo Figura 8”, CIENCIA ergo–sum 17 (2010), No. 3, 307–312.
[8] Anaya J.G., Maya D. and Orozco-Zitli F., “Making holes in the second symmetric products of a cyclicly connected graph”, Journal of Mathematics Research 6 (2014), No. 3, 105–113.
[9] Anaya J.G., Maya D. and Orozco-Zitli F., “Making holes in the second symmetric products of dendrites and some fan”, CIENCIA ergo–sum 19 (2012), No.1, 83–92.
[10] Anaya J.G., Maya D. and Orozco-Zitli F., “Making holes in the second symmetric product of unicoherent locally connected continua”, Topology Proc. 48 (2016), 251–259.
[11] Borsuk K., “Quelques théorémes sur les ensembles unicoherents”, Fund. Math. 17 (1931), No.1, 171–209.
[12] Castañeda E., “A Unicoherent Continuum Whose Second Symmetric Product is not Unicoherent”, Topology Proc. 23 (1998), 61–67.
[13] Eilenberg S., “Sur les transformations d’espaces métriques en circonférence”, Fund. Math. 24 (1935), No.1, 160–176.
[14] Eilenberg S., “Transformations continues en circonférence et la topologie du plan”, Fund. Math. 26 (1936), No. 1, 61–112.
[15] Ganea T., “Covering spaces and cartesian products”, Ann. Soc. Polon. Math. 25 (1952), 30–42.
[16] Ganea T., “Symmetrische Potenzen topologischer Raume”, Math. Nachr. 11 (1954), No. 4-5, 305–316.
[17] García-Máynez A. and Illanes A., “A survey on unicoherence and related properties”, An. Inst. Mat., Univ. Nac. Autón. Méx. 29 (1989), 17–67.
[18] Illanes A., “Multicoherence of Whitney levels”, Topology Appl. 68 (1996), No.3, 251–265.
[19] Illanes A., “The hyperspace C2(X) for a finite graph X is unique”, Glas. Mat. Ser. III 37 (2002), 347–363.
[20] Illanes A. and Nadler S. B., Jr., Hyperspaces, Fundamentals and Recent Advances, Monographs and Textbooks in Pure and Applied Mathematics, 216, Marcel Dekker, New York, 1999.
[21] Kuratowski K., “Sur les continus de Jordan et le théoréme de M. Brouwer”, Fund. Math. 8 (1926), No. 1, 137–150.
[22] Kuratowski K., “Une carecterisation topologique de la surface de la sphére”, Fund. Math. 13 (1929), No. 1, 307–318.
[23] Macías S., “On symmetric products of continua”, Topology Appl. 92 (1999), No. 2, 173–182.
[24] Macías S., “On the hyperspaces Cn(X) of a continuum X”, Topology Appl. 109 (2001), 237–256.
[25] Mardešić S., “Equivalence of singular and Čech homology for ANR-s. Application to unicoherence”, Fund. Math. 46 (1958), No. 1, 29–45.
[26] Nadler Jr. S.B., “Arc components of certain chainable continua”, Canad. Math. Bull. 14 (1971), 183–189.
[27] Nadler Jr. S.B., Continuum Theory, An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, Inc., New York, 1992.
[28] Nadler Jr. S.B., “Continua whose cone and hyperspace are homeomorphic”, Trans. Amer. Math. Soc. 230 (1977), 321–345.
[29] Nadler Jr. S.B., Hyperspace of sets, Monographs and Textbooks in Pure and Applied Mathematics, 49, Marcel Dekker, New York, 1978.
[30] Whyburn G.T., Analytic Topology, AMS Colloquium Publications, 28, Providence, R.I., 1942.
[2] Anaya J.G., “Making holes in the hyperspaces of a Peano continuum”, Topology Proc. 37 (2011), 1–14.
[3] Anaya J.G., Carranza R.I., Maya D. and Orozco-Zitli F., “Making holes in the hyperspace of subcontinua of smooth dendroids”, Preprint.
[4] Anaya J.G., Castañeda-Alvarado E. and Orozco-Zitli F., “Making holes in the hyperspace of subcontinua of some continua”, Adv. in Pure Math. 2 (2012), 133–138.
[5] Anaya J.G., Castañeda-Alvarado E., Fuentes-Montes de Oca A. and Orozco-Zitli F., “Making holes in the cone, suspension and hyperspaces of some continua”, Comment. Math. Univ. Carolin. 59 (2018), No. 3, 343–364.
[6] Anaya J.G., Castañeda-Alvarado E., Fuentes-Montes de Oca A. and Orozco-Zitli F., “Making holes in the hyperspaces suspension of some continua”, Preprint.
[7] Anaya J.G., Maya D. y Orozco-Zitli F., “Agujeros en el segundo producto simétrico de subcontinuos del continuo Figura 8”, CIENCIA ergo–sum 17 (2010), No. 3, 307–312.
[8] Anaya J.G., Maya D. and Orozco-Zitli F., “Making holes in the second symmetric products of a cyclicly connected graph”, Journal of Mathematics Research 6 (2014), No. 3, 105–113.
[9] Anaya J.G., Maya D. and Orozco-Zitli F., “Making holes in the second symmetric products of dendrites and some fan”, CIENCIA ergo–sum 19 (2012), No.1, 83–92.
[10] Anaya J.G., Maya D. and Orozco-Zitli F., “Making holes in the second symmetric product of unicoherent locally connected continua”, Topology Proc. 48 (2016), 251–259.
[11] Borsuk K., “Quelques théorémes sur les ensembles unicoherents”, Fund. Math. 17 (1931), No.1, 171–209.
[12] Castañeda E., “A Unicoherent Continuum Whose Second Symmetric Product is not Unicoherent”, Topology Proc. 23 (1998), 61–67.
[13] Eilenberg S., “Sur les transformations d’espaces métriques en circonférence”, Fund. Math. 24 (1935), No.1, 160–176.
[14] Eilenberg S., “Transformations continues en circonférence et la topologie du plan”, Fund. Math. 26 (1936), No. 1, 61–112.
[15] Ganea T., “Covering spaces and cartesian products”, Ann. Soc. Polon. Math. 25 (1952), 30–42.
[16] Ganea T., “Symmetrische Potenzen topologischer Raume”, Math. Nachr. 11 (1954), No. 4-5, 305–316.
[17] García-Máynez A. and Illanes A., “A survey on unicoherence and related properties”, An. Inst. Mat., Univ. Nac. Autón. Méx. 29 (1989), 17–67.
[18] Illanes A., “Multicoherence of Whitney levels”, Topology Appl. 68 (1996), No.3, 251–265.
[19] Illanes A., “The hyperspace C2(X) for a finite graph X is unique”, Glas. Mat. Ser. III 37 (2002), 347–363.
[20] Illanes A. and Nadler S. B., Jr., Hyperspaces, Fundamentals and Recent Advances, Monographs and Textbooks in Pure and Applied Mathematics, 216, Marcel Dekker, New York, 1999.
[21] Kuratowski K., “Sur les continus de Jordan et le théoréme de M. Brouwer”, Fund. Math. 8 (1926), No. 1, 137–150.
[22] Kuratowski K., “Une carecterisation topologique de la surface de la sphére”, Fund. Math. 13 (1929), No. 1, 307–318.
[23] Macías S., “On symmetric products of continua”, Topology Appl. 92 (1999), No. 2, 173–182.
[24] Macías S., “On the hyperspaces Cn(X) of a continuum X”, Topology Appl. 109 (2001), 237–256.
[25] Mardešić S., “Equivalence of singular and Čech homology for ANR-s. Application to unicoherence”, Fund. Math. 46 (1958), No. 1, 29–45.
[26] Nadler Jr. S.B., “Arc components of certain chainable continua”, Canad. Math. Bull. 14 (1971), 183–189.
[27] Nadler Jr. S.B., Continuum Theory, An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, Inc., New York, 1992.
[28] Nadler Jr. S.B., “Continua whose cone and hyperspace are homeomorphic”, Trans. Amer. Math. Soc. 230 (1977), 321–345.
[29] Nadler Jr. S.B., Hyperspace of sets, Monographs and Textbooks in Pure and Applied Mathematics, 49, Marcel Dekker, New York, 1978.
[30] Whyburn G.T., Analytic Topology, AMS Colloquium Publications, 28, Providence, R.I., 1942.