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L-approach merotopies and their categorical perspective

Khare M., Tiwari S.

Demonstratio Mathematica

2012

Vol. 45, nr 3

699-716

In the present paper, we have made a category theoretic and lattice theoretic study of some nearness-like structures in the L-approach theory. Using L-grills, the notion of L-approach grill structure is introduced as a characterization of L-approach grill merotopy on X; their categorical perspectives and implications are also investigated. A number of illustrative examples are included.

Inverse sequences and absolute co-extensors

Ivanšic I., Rubin R.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 3

243-259

Suppose that K is a CW-complex, X is an inverse sequence of stratifiable spaces, and X = lim X. Using the concept of semi-sequence, we provide a necessary and sufficient condition for X to be an absolute co-extensor for K in terms of the inverse sequence X and without recourse to any specific properties of its limit. To say that X is an absolute co-extensor for K is the same as saying that K is an absolute extensor for X, i.e., that each map ƒ : A → K from a closed subset A of X extends to a map F : X → K. Incase K is & polyhedron |/C|cw (the set \K\ with the weak topology CW), we determine a similar characterization that takes into account the simplicial structure of K.