IJPAM: Volume 117, No. 2 (2017)

Title

PROXIMATE AND APPROXIMATE SEQUENCES

Authors

Zoran Misajleski
Department of Mathematics
Faculty of Civil Engineering
Ss. Cyril and Methodius University
9, Goce Delcev blvd., 1000 Skopje, MACEDONIA

Abstract

In this paper the author defines and discuses the concept of approximate sequences. First, in a separate section, he discusses proximate and approximate sequences.

After that he presents some properties of approximate sequences that are anoloqous to similar results for fundamental sequences, established in previous paper [1] titled equivalence of intrinsic shape, based on V-continuous functions and shape (N. Shekutkovski, Z. Misajleski, G. Markoski, M. Shoptrajanov, Bulletin mathematique, 2013, No. 1, 39-48). The author gives an optional definition of the function $r_{\cal V}$, with the help of intersections, which in [1] is defined using notion of depth. Also he shows that in a compact metric space there exists a cofinal sequence of finite regular coverings. In addition he shows that it is possible to choose the images of functions of approximate as subsets of the union of elements of such a sequence of coverings. Furthermore, analogue theorems of [1], which refers to approximate instead for fundamental sequences, he present and prove. Finally, the author shows that shape category constructed with the classes of approximate sequences, is equivalent with the intrinsic shape category constructed with the classes of proximate sequences.

History

Received: 2017-06-14
Revised: 2017-11-15
Published: December 23, 2017

AMS Classification, Key Words

AMS Subject Classification: 54C56
Key Words and Phrases: shape theory, function $r_{\cal V}$, cofinal sequence of finite coverings, proximate sequence, approximate sequence, equivalence

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Bibliography

1
N. Shekutkovski, Z. Misajleski, G. Markoski, M. Shoptrajanov, Equvalence of intristic shape, based on $V$-continuous functions and shape, Bulletin mathematique, 1, (2013), 39-48.

2
N. Shekutkovski, Intristic definition of strong shape for compact metric spaces, Topology Proceedings, 39, (2012), 27-39.

3
K. Borsuk, Teorija shejpov, Izdateljstvo Mir, Moskva, (1976).

4
J. M. R. Sanjurjo, A non continuous description of the shape, Quart. J. Math. Oxford Ser., 40, (1989), 351-359.

5
N. Shekutkovski, Z. Misajleski, Intristic shape based on $\varepsilon$-continuity and on continuiuty up to a covering are equivalent, Proceedings of FMNS 2011, 1, (2011), 77-82.

6
N. Shekutkovski, Z. Misajleski, Intristic shape based on $\varepsilon$-continuity and on contiuity up to a covering are equivalent (II), Proceedings of FMNS 2013, 1, (2013), 87-94.

7
N. Shekutkovski, Z. Misajleski, Equivalence of intristic shape and shape, God. Zb. Inst. Mat., 42, (2013), 69-80.

How to Cite?

DOI: 10.12732/ijpam.v117i2.9 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 117
Issue: 2
Pages: 355 - 365


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