AN ALTERNATE PROOF OF CLOSED MAPPING IN TOPOLOGY
The write-up seek to find alternative proof(s) to closed bijective mappings in topol-
ogy given that;
Let x and y be topological spaces and f : x → y a mapping f is called a closed
mapping if f(H) is closed in y for every closed set H in x.
Let x and y be topological spaces and f : x → y a bijective mapping, the f is open ⇐⇒ f is closed.
In general function which are open need not to be closed and vice versa. In other
words, a mapping is closed if it carries closed sets over to closed sets.
This paper gives alternate proofs to closed bijective mappings in topology.
 B. Margherita, ”Closed Map.” From MathWorld–A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/ClosedMap.html . Last accessed, 10th October, 2019
 Schochetman I. E., “A characterization of open mapping in terms of convergent sequences,” International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 76162, 5 pages, 2006. View at Google Scholar. Last accessed, 10th October, 2019
 Dugundji J. Topology, Prentice Hall, New Delhi, India, 1975. Last accessed, 10th October, 2019
 Lee J. M. (2003) Introduction to smooth Manifolds. Graduate Texts in Mathematics. 218. Springer Science and Business Media, pg. 550
 Munkres, J. R. (2000). Topology (2nd edition) Prentice hall, pg19
 John R. ”Continuous Map.” From MathWorld–A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/ContinuousMap.html.Last accessed, 10th October, 2019.
 Ponomarev V.I (originator),Encyclopedia of mathematics.
 https://www.emathzone.com/tutorials/general-topology/open-mapping-and-closed-mapping.html ixzz62vHwOXEd Last accessed, 20th November, 2019