On the Limits of Proximate Sequences.

Download PDF

Authors: A. BUKLLA

DOI: 10.46793/KgJMat2307.1087B


We investigate the continuity of the pointwise limits of proximate sequences. Both general proximate sequences and a subclass are considered. We obtain some results related to the fixed points of the limit functions and fixed point like properties of the proximate sequences.


intrinsic shape, proximate sequence, limit function, fixed point property.


[1]   K. Borsuk, Theory of Shape, Polish Scientific Publisher, Warszawa, 1975.

[2]   N. Shekutkovski, Intrinsic definition of strong shape for compact metric spaces, Topology Proc. 39 (2012), 27–39.

[3]   N. Shekutkovski, Intrinsic shape - The proximate approach, Filomat 29(10) (2015), 2199–2205. https://doi.org/10.2298/FIL1510199S

[4]   N. Shekutkovski, Z. Misajleski, Gj. Markoski and M. Shoptrajanov, Equivalence of intrinsic shape, based on V -continuous functions, and shape, Bulletin Mathematique 1 (2013), 39–48.

[5]   R. J. Pawlak, On some properties of the spaces of almost continuous functions, Int. J. Math. Math. Sci. 19(1) (1996), 19–24.

[6]   A. Buklla and Gj. Markoski, Proximately chain refinable functions, Hacet. J. Math. Stat. 48(5) (2019), 1437–1442. https://doi.org/10.15672/HJMS.2018.584