## What is/are Open Mapping?

Open Mapping - Moreover, the version of open mapping theorem in the class of topological rough group is obtained.^{[1]}Hence, many important results in functional analysis, like the Banach-Steinhaus theorem, the open mapping theorem and the closed graph theorem, hold for the $${\cal H}{\cal K}$$ (X) space.

^{[2]}We describe the points of discontinuity in terms of open mapping theorems and eigenvalue crossings.

^{[3]}The open mapping theorem and the principle of maximum of the norm for a p-holomorphic function and the uniqueness theorem are proved.

^{[4]}We introduce δ-irresolute, δ-closed, pre-δ-open and pre -δ-closed mappings and investigate properties and characterizations of these new types of mappings and also explore further properties of the well-known notions of δ-continuous and δ-open mappings.

^{[5]}Many authors consider that the main pillars of Functional Analysis are the Hahn–Banach Theorem, the Uniform Boundedness Principle and the Open Mapping Principle.

^{[6]}However, the quality and the amount of rural building annotated data in open mapping services like OpenStreetMap (OSM) is not sufficient for training accurate models for such detection.

^{[7]}The focus of this paper is on exploring the fit for purpose of semantic segmentation techniques to feed and update existing road network datasets and traffic sign censuses, exploiting free and open mapping initiative like Mapillary (possibly including commercial derivative products) and OpenStreetMap (OSM).

^{[8]}We established order-preserving versions of the basic principles of functional analysis such as Hahn-Banach, Banach-Steinhaus, open mapping and Banach-Alaoglu theorems.

^{[9]}El-Deeb, α-continuous and α-open mappings, Acta Math.

^{[10]}In order to obtain results like the Open Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Theorem, H.

^{[11]}The following results are obtained: (1) Every sp-network is preserved by a continuous pseudo-open mapping.

^{[12]}In fact, this theorem follows from a more general result about spaces with an ω-directed lattice of d-open mappings.

^{[13]}To get the main result, which is based on set separation arguments, we prove an open mapping result valid for Quasi-Differential-Quotient (QDQ) approximating cones, a notion of 'tangent cone' resulted as a peculiar specification of H.

^{[14]}In this article the concepts of somewhat pairwise fuzzy irresolute and somewhat pairwise fuzzy irresolute semiopen mappings are introduced.

^{[15]}

## pairwise weakly fuzzy

The aim of this paper is to introduce some pairwise weakly fuzzy mappings, called pairwise weakly fuzzy δ-semi-pre-continuous mappings and pairwise weakly fuzzy δ-semi pre-open mappings in fuzzy bitopological spaces.^{[1]}

## neutrosophic crisp semi

This work employs the conceptions of neutrosophic crisp a-open and semi-a-open sets to distinguish some novel forms of weakly neutrosophic crisp open mappings; for instance, neutrosophic crisp a-open mappings, neutrosophic crisp a*-open mappings, neutrosophic crisp a**-open mappings, neutrosophic crisp semi-a-open mappings, neutrosophic crisp semi-a*-open mappings, and neutrosophic crisp semi-a**-open mappings.^{[1]}

## continuous mappings pairwise

The concepts of different mappings such as pairwise fuzzy I -continuous mappings, pairwise fuzzy D -continuous mappings, pairwise fuzzy B -continuous mappings, pairwise fuzzy I -open mappings, pairwise fuzzy D -open mappings, pairwise fuzzy B -open mappings, pairwise fuzzy I -closed mappings, pairwise fuzzy D -closed mappings and pairwise fuzzy B -closed mappings have been introduced.^{[1]}

## open mapping theorem

Moreover, the version of open mapping theorem in the class of topological rough group is obtained.^{[1]}Hence, many important results in functional analysis, like the Banach-Steinhaus theorem, the open mapping theorem and the closed graph theorem, hold for the $${\cal H}{\cal K}$$ (X) space.

^{[2]}We describe the points of discontinuity in terms of open mapping theorems and eigenvalue crossings.

^{[3]}The open mapping theorem and the principle of maximum of the norm for a p-holomorphic function and the uniqueness theorem are proved.

^{[4]}Then, as applications we will obtain open mapping theorems and continuation principles for these classes of mappings.

^{[5]}In order to obtain results like the Open Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Theorem, H.

^{[6]}The roots of this concept go back to a circle of fundamental regularity ideas from classical analysis embodied in such results as the implicit function theorem, the Banach open mapping theorem, and theorems of Lyusternik and Graves, on the one hand, and Sard’s theorem and transversality theory, on the other hand.

^{[7]}