On ideal sequence covering maps

Sudip Kumar Pal, Nayan Adhikary, Upasana Samanta


 In this paper we introduce the concept of ideal sequence covering map which is a generalization of sequence covering map, and investigate some of its properties. The present article contributes to the problem of characterization to the certain images of metric spaces which posed by Y. Tanaka [22], in more general form. The entire investigation is performed in the setting of ideal convergence extending the recent results in [11,15,16]. 


sequence covering; sequentially quotient; sn-networks; boundary compact map; ideal convergence

Subject classification

54C10; 40A05; 54E35.

Full Text:



A. Arhangelskii, Some types of factor mappings and the relation between classes of topological spaces, Soviet Math. Dokl. 4 (1963), 1726-1729.

J. Chaber, Mappings onto metric spaces, Topology Appl. 14 (1982), 31-42. https://doi.org/10.1016/0166-8641(82)90045-1

H. Fast, Sur Ia convergence Statistique, Colloq. Math. 2 (1951), 241-244. https://doi.org/10.4064/cm-2-3-4-241-244

S. P. Franklin, Spaces in which sequence suffice, Fund. Math. 57 (1965) 107-115. https://doi.org/10.4064/fm-57-1-107-115

J. A. Fridy, On ststistical convergence, Analysis 5 (1985), 301-313. https://doi.org/10.1524/anly.1985.5.4.301

P. Kostyrko, T. Salát and W. Wilczynski, $mathcal{I}$-convergence, Real Analysis Exchange 26, no. 2 (2000-2001), 669-686.

B. K. Lahiri and P. Das, I and I*-convergence in topological spaces, Math. Bohem. 130 (2005), 153-160.

S. Lin, Point-countable Covers and Sequence-covering Mappings (in Chinese), Science Press, Beijing, 2002.

F. Lin and S. Lin, On sequence-covering boundary compact maps of metric spaces, Adv. Math. (China) 39, no. 1 (2010), 71-78.

F. Lin and S. Lin, Sequence-covering maps on generalized metric spaces, Houston J. Math. 40, no. 3 (2014), 927-943.

S. Lin and P. Yan, Sequence-covering maps of metric spaces, Topology Appl. 109 (2001), 301-314. https://doi.org/10.1016/S0166-8641(99)00163-7

G. D. Maio and Lj.D.R. Kocinac, Statistical convergence in topology, Topology Appl. 156 (2008), 28-45. https://doi.org/10.1016/j.topol.2008.01.015

E. Michael, A quintuple quotient quest, General Topology Appl. 2 (1972), 91-138. https://doi.org/10.1016/0016-660X(72)90040-2

T. Nogura and Y. Tanaka, Spaces which contains a copy of Sω or S2 , and their applications, Topology Appl. 30 (1988), 51-62. https://doi.org/10.1016/0166-8641(88)90080-6

V. Renukadevi and B. Prakash, On statistically sequentially covering maps, Filomat 31, no. 6 (2017), 1681-1686. https://doi.org/10.2298/FIL1706681R

V. Renukadevi and B. Prakash, On statistically sequentially quotient maps, Korean J. Math. 25, no. 1 (2017), 61-70.

T. Salát, On statistically convergent sequences of real numbers, Math. Slovaca. 30, no. 2 (1980), 139-150.

M. Scheepers, Combinatorics of open covers(I): Ramsey theory, Topology Appl. 69 (1996), 31-62. https://doi.org/10.1016/0166-8641(95)00067-4

I. J. Schoenberg, The integrability of certain function and related summability methods Amer. Math. Monthly 66 (1959), 361-375. https://doi.org/10.2307/2308747

F. Siwiec, Sequence-covering and countably bi-quotient maps, General Topology Appl. 1 (1971), 143-154. https://doi.org/10.1016/0016-660X(71)90120-6

F. Siwiec, Generalizations of the first axiom of countability, Rocky Mountain J. Math. 5 (1975), 1-60. https://doi.org/10.1216/RMJ-1975-5-1-1

Y. Tanaka, Point-countable covers and k-networks, Topology Proc. 12 (1987), 327-349.

J. E. Vaughan, Discrete sequences of points, Topology Proc. 3 (1978), 237-265.

P. F. Yan, S. Lin and S. L. Jiang, Metrizability is preserved by closed sequence-covering maps, Acta Math. Sinica. 47 (2004), 87-90.

P. F. Yan and C. Lu, Compact images of spaces with a weaker metric topology, Czech. Math. j. 58, no. 4 (2008), 921-926. https://doi.org/10.1007/s10587-008-0060-5

A. Zygmund, Trigonometric Series, Cambridge Univ. Press, Cambridge, UK (1979).

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM


Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. On I-quotient mappings and I-cs'-networks under a maximal ideal
Xiangeng Zhou
Applied General Topology  vol: 21  issue: 2  first page: 235  year: 2020  
doi: 10.4995/agt.2020.12967

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt