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Fréchet–Urysohn subspaces of free topological groups

open access: yesFréchet–Urysohn subspaces of free topological groups
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COUNTABLE-CODIMENSIONAL SUBSPACES OF TOPOLOGICAL VECTOR SPACES

open access: yesCOUNTABLE-CODIMENSIONAL SUBSPACES OF TOPOLOGICAL VECTOR SPACES
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Fréchet-Urysohn subspaces of free topological groups, II

Topology and its Applications, 2019
The author completes his classification, for metrizable spaces $X$, of when the subspace $F_n(X)$ (of words of length at most $n$) of the free topological group on $X$ is Fréchet-Urysohn. The space $F_2(X)$ is Fréchet-Urysohn [\textit{K. Yamada}, Topol. Proc.
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Photonic topological subspace-induced bound states in the continuum

Optics Letters, 2023
Bound states in the continuum (BICs) are intriguing localized states that possess eigenvalues embedded within the continuum of extended states. Recently, a combination of topological band theory and BIC physics has given rise to a novel form of topological matter known as topological BICs.
Wenchao Yan   +3 more
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An abstract theory of topological subspaces

Mathematical Proceedings of the Cambridge Philosophical Society, 1964
1. Introduction. The open subsets of a topological space X form a complete Brouwerian, i.e. distributive and pseudo-complemented lattice L(X). Many topological properties of X can be formulated as properties of L(X), although, in general, X is not determined by L(X). Obvious examples are quasi-compactness and connectivity: X is quasi-compact if any set
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Existence of a topological subspace in apparently non-topological systems

2016 Progress in Electromagnetic Research Symposium (PIERS), 2016
It is well known that inversion symmetry in one-dimensional periodic systems leads to the quantization of the Zak phase, which is either 0 or π. When the system has particle-hole symmetry, this topological property ensures the existence of zero-energy interface states at the interface of two bulk systems with different Zak phases.
null Yixin Xiao   +2 more
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Compactness and subspace M-topologies

Soft Computing, 2022
P. Rajish Kumar   +2 more
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